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Journal articles on the topic 'R-convexité'

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Published: 7 July 2024

Last updated: 7 July 2024

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1

Asserda, S. "Convexité holomorphe intermédiaire des revetements d'un domaine pseudoconvexe." Bulletin of the Australian Mathematical Society 56, no. 2 (October 1997): 285–90. http://dx.doi.org/10.1017/s0004972700031038.

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Let M be a complex manifold and L → M be a positive holomorphic line bundle over M equipped with a Hermitian metric h of class C2. If D ⊂⊂ M is a pseudoconvex domain which is relatively compact in M then there exists an integer r0 such that for every r ≥ r0 and for every connected holomorphic covering π: the covering is holomorphically convex with respect to holomorphic sections of .

2

Zhang, Tao, Alatancang Chen, Bo-Yan Xi, and Huan-Nan Shi. "The relationship between r-convexity and Schur-convexity and its application." Journal of Mathematical Inequalities, no. 3 (2023): 1145–52. http://dx.doi.org/10.7153/jmi-2023-17-74.

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3

Zhao, Feng-Zhen. "The log-convexity of $r$-derangement numbers." Rocky Mountain Journal of Mathematics 48, no. 3 (June 2018): 1031–42. http://dx.doi.org/10.1216/rmj-2018-48-3-1031.

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4

Nikoufar, Ismail. "A Perspective Approach for Characterization of Lieb Concavity Theorem." Demonstratio Mathematica 49, no. 4 (December 1, 2016): 463–69. http://dx.doi.org/10.1515/dema-2016-0040.

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Abstract Lieb’s extension theorem holds for generalized p + q ∈ [0; 1] and Ando convexity theorem holds for q - r > 1. In this paper, we give a complete characterization for concavity or convexity of Lieb well known theorem in the case where p + q ≥ 1 or p+q ≤ 0. We also characterize some auxiliary results including Ando theorem for q-r ≤ 1.

5

Quast, Peter, and Makiko Sumi Tanaka. "Convexity of reflective submanifolds in symmetric $R$-spaces." Tohoku Mathematical Journal 64, no. 4 (2012): 607–16. http://dx.doi.org/10.2748/tmj/1356038981.

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6

Hou, Qing-Hu, and Zuo-Ru Zhang. "Asymptotic r-log-convexity and P-recursive sequences." Journal of Symbolic Computation 93 (July 2019): 21–33. http://dx.doi.org/10.1016/j.jsc.2018.04.012.

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7

Yu-Liang, Shen. "On the weak uniform convexity of $Q(R)$." Proceedings of the American Mathematical Society 124, no. 6 (1996): 1879–82. http://dx.doi.org/10.1090/s0002-9939-96-03317-5.

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8

Rekic-Vukovic, Amra, and Nermin Okicic. "A convexity in R^2 with river metric." Gulf Journal of Mathematics 15, no. 2 (November 12, 2023): 25–39. http://dx.doi.org/10.56947/gjom.v15i2.1226.

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In this paper we consider the space R2 with the river metric d* and different types of convexity of this space. We define W-convex structure in (R2, d*) and we give the complete characterization of the convex sets in this space. We consider some measures of noncompactness and we give the moduli of noncompactness for considered measures on this space.

9

Sayed, Osama, El-Sayed El-Sanousy, and Yaser Sayed. "On (L,M)-fuzzy convex structures." Filomat 33, no. 13 (2019): 4151–63. http://dx.doi.org/10.2298/fil1913151s.

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This paper defines a new class of L-fuzzy sets called r-L-fuzzy biconvex sets in (L,M)-fuzzy convex structures (X,C), where C is an (L,M)-fuzzy convexity on X, and some of their properties were studied. In addition, weintroduce (L,M)-fuzzy topological convexity space and study some of its properties. Finally, we introduce locally (L,M)-fuzzy topology (L,M)-fuzzy convexity space and study some of its properties.

10

Almutairi, Ohud, and Adem Kılıçman. "Generalized Integral Inequalities for Hermite–Hadamard-Type Inequalities via s-Convexity on Fractal Sets." Mathematics 7, no. 11 (November 6, 2019): 1065. http://dx.doi.org/10.3390/math7111065.

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In this article, we establish new Hermite–Hadamard-type inequalities via Riemann–Liouville integrals of a function ψ taking its value in a fractal subset of R and possessing an appropriate generalized s-convexity property. It is shown that these fractal inequalities give rise to a generalized s-convexity property of ψ . We also prove certain inequalities involving Riemann–Liouville integrals of a function ψ provided that the absolute value of the first or second order derivative of ψ possesses an appropriate fractal s-convexity property.

11

Geschke, Stefan, and Menachem Kojman. "Convexity numbers of closed sets in $\mathbb R^n$." Proceedings of the American Mathematical Society 130, no. 10 (March 25, 2002): 2871–81. http://dx.doi.org/10.1090/s0002-9939-02-06437-7.

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12

Simić, Slavko, Sara Salem Alzaid, and Hassen Aydi. "On the symmetrized s-divergence." Open Mathematics 18, no. 1 (May 26, 2020): 378–85. http://dx.doi.org/10.1515/math-2020-0027.

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Abstract In this study, we work with the relative divergence of type s,s\in {\mathbb{R}} , which includes the Kullback-Leibler divergence and the Hellinger and χ 2 distances as particular cases. We study the symmetrized divergences in additive and multiplicative forms. Some basic properties such as symmetry, monotonicity and log-convexity are established. An important result from the convexity theory is also proved.

13

Sokół, Janusz, and Katarzyna Trabka-Wiȩcław. "Radius problems for univalent functions." Journal of Applied Analysis 26, no. 1 (June 1, 2020): 111–15. http://dx.doi.org/10.1515/jaa-2020-2008.

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AbstractThis paper considers the following problem: for what value r, {r<1} a function that is univalent in the unit disk {|z|<1} and convex in the disk {|z|<r} becomes starlike in {|z|<1}. The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered.

14

Huotari, Robert, and Junning Shi. "Support cones and convexity of sets in ${\mathbb {R}}^n$." Proceedings of the American Mathematical Society 124, no. 8 (August 1, 1996): 2405–14. http://dx.doi.org/10.1090/s0002-9939-96-03347-3.

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15

Şahin, Hasan, and İsmet Yildiz. "Determination of some properties of starlike and close-to-convex functions according to subordinate conditions with convexity of a certain analytic function." Ukrains’kyi Matematychnyi Zhurnal 75, no. 7 (July 25, 2023): 995–1008. http://dx.doi.org/10.37863/umzh.v75i7.7214.

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UDC 517.5 Investigation of the theory of complex functions is one of the most fascinating aspects of theory of complex analytic functions of one variable. It has a huge impact on all areas of mathematics. Many mathematical concepts are explained when viewed through the theory of complex functions. Let f ( z ) ∈ A , f ( z ) = z + ∑ n ≥ 2 ∞ a n z n , be an analytic function in the open unit disc normalized by f ( 0 ) = 0 and f ' ( 0 ) = 1. For close-to-convex and starlike functions, new and different conditions are obtained by using subordination properties, where r is a positive integer of order 2 - r ( 0 < 2 - r ≤ 1 2 ) . By using subordination, we propose a criterion for f ( z ) ∈ S * [ a r , b r ] . The relations for starlike and close-to-convex functions are investigated under certain conditions according to their subordination properties. At the same time, we analyze the convexity of some analytic functions and study their regional transformations. In addition, the properties of convexity for f ( z ) ∈ A are examined.

16

Cai, Chuan-Yu, Lu Chen, Ti-Ren Huang, and Yuming Chu. "New properties for the Ramanujan R-function." Open Mathematics 20, no. 1 (January 1, 2022): 724–42. http://dx.doi.org/10.1515/math-2022-0045.

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Abstract In the article, we establish some monotonicity and convexity (concavity) properties for certain combinations of polynomials and the Ramanujan R-function by use of the monotone form of L’Hôpital’s rule and present serval new asymptotically sharp bounds for the Ramanujan R-function that improve some previously known results.

17

Sil, Swarnendu. "Calculus of variations: A differential form approach." Advances in Calculus of Variations 12, no. 1 (January 1, 2019): 57–84. http://dx.doi.org/10.1515/acv-2016-0058.

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AbstractWe study integrals of the form {\int_{\Omega}f(d\omega_{1},\dots,d\omega_{m})}, where {m\geq 1} is a given integer, {1\leq k_{i}\leq n} are integers, {\omega_{i}} is a {(k_{i}-1)}-form for all {1\leq i\leq m} and {f:\prod_{i=1}^{m}\Lambda^{k_{i}}(\mathbb{R}^{n})\rightarrow\mathbb{R}} is a continuous function. We introduce the appropriate notions of convexity, namely vectorial ext. one convexity, vectorial ext. quasiconvexity and vectorial ext. polyconvexity. We prove weak lower semicontinuity theorems and weak continuity theorems and conclude with applications to minimization problems. These results generalize the corresponding results in both classical vectorial calculus of variations and the calculus of variations for a single differential form.

18

Cholaquidis, Alejandro. "A counter example on a Borsuk conjecture." Applied General Topology 24, no. 1 (April 5, 2023): 125–28. http://dx.doi.org/10.4995/agt.2023.18176.

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The study of shape restrictions of subsets of Rd has several applications in many areas, being convexity, r-convexity, and positive reach, some of the most famous, and typically imposed in set estimation. The following problem was attributed to K. Borsuk, by J. Perkal in 1956:find an r-convex set which is not locally contractible. Stated in that way is trivial to find such a set. However, if we ask the set to be equal to the closure of its interior (a condition fulfilled for instance if the set is the support of a probability distribution absolutely continuous with respect to the d-dimensional Lebesgue measure), the problem is much more difficult. We present a counter example of a not locally contractible set, which is r-convex. This also proves that the class of supports with positive reach of absolutely continuous distributions includes strictly the class ofr-convex supports of absolutely continuous distributions.

19

Házy, Attila, and Judit Makó. "Counter-examples to Breckner-convexity." Multidiszciplináris Tudományok 13, no. 3 (December 15, 2023): 74–80. http://dx.doi.org/10.35925/j.multi.2023.3.8.

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In this paper, we examine convexity type inequalities. Let D be a nonempty convex subset of a linear space, c>0 and α:D-D→R be a given even function. The inequality f((x+y)/2) ≤ c f(x) + c f(y) + α(x-y) (x,y € D) is the focus of our examinations. We will construct an example to show that for c=1, this Jensen type inequality does not imply the convexity of the function. Then, we compare this inequality with Hermite–Hadamard type inequalities.

20

Sofonea, Daniel, Ioan Ţincu, and Ana Acu. "Convex sequences of higher order." Filomat 32, no. 13 (2018): 4655–63. http://dx.doi.org/10.2298/fil1813655s.

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In this paper we study the class of convex sequences of higher order defined using the difference operators and investigate their properties. The notion of the convex sequence of order r ? N will be extended for r a real number. Some necessary and sufficient conditions such that a real sequence belongs to the class of convex sequences of higher order r ? R are introduced. Using different types of means we will investigate the convexity of higher order for real sequences.

21

Huang, Ti Ren, Lu Chen, Shen-Yang Tan, and Yuming Chu. "Monotonicity, convexity and bounds involving the beta and Ramanujan R-functions." Journal of Mathematical Inequalities, no. 2 (2021): 615–28. http://dx.doi.org/10.7153/jmi-2021-15-45.

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22

Geschke, Stefan. "More on convexity numbers of closed sets in $\mathbb{R}^n$." Proceedings of the American Mathematical Society 133, no. 5 (May 1, 2005): 1307–15. http://dx.doi.org/10.1090/s0002-9939-04-07685-3.

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23

Jiao, Hongwei, Yunrui Guo, and Fenghui Wang. "Modulus of Convexity, the CoeffcientR(1,X), and Normal Structure in Banach Spaces." Abstract and Applied Analysis 2008 (2008): 1–5. http://dx.doi.org/10.1155/2008/135873.

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LetδX(ϵ)andR(1,X)be the modulus of convexity and the Domínguez-Benavides coefficient, respectively. According to these two geometric parameters, we obtain a sufficient condition for normal structure, that is, a Banach spaceXhas normal structure if2δX(1+ϵ)>max{(R(1,x)-1)ϵ,1-(1-ϵ/R(1,X)-1)}for someϵ∈[0,1]which generalizes the known result by Gao and Prus.

24

Lim, Eunji, and Elizabeth Tavarez. "Nonparametric Tests for Convexity/Monotonicity/Positivity of Multivariate Functions with Noisy Observations." International Journal of Statistics and Probability 6, no. 5 (July 20, 2017): 18. http://dx.doi.org/10.5539/ijsp.v6n5p18.

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We propose a new method of testing for a function's convexity, monotonicity, or positivity, based on some noisy observations of the function made over a finite set $\mathcal{T}$ of points in the domain, where the observations can be made multiple times at each point in $\mathcal{T}$. One of the traditional approaches to the test of a function's shape characteristic is to fit a convex, a monotone, or a positive function, depending on the shape characteristic we wish to test for, to the data set minimizing the sum of squared errors, and to compute the sum of squared differences (SSD) between the fit and the data set. While the traditional approach proceeds by observing the SSD as the number of points in $\mathcal{T}$ increases to infinity, we propose observing the SSD as $r$, the number of observations taken at each point in $\mathcal{T}$, increases to infinity. This new way of observing the asymptotic behavior of the SSD leads to a test procedure that does not require the estimation of any additional parameters, and hence, is easy to implement. The proposed test procedure is proven to achieve a prescribed power as $r \rightarrow \infty$. Numerical examples illustrate that the proposed test successfully detects the convexity/monotonicity/positivity of a function, as well as the non-convexity/non-monotonicity/non-positivity of a function.

25

Hall, R. L., and W. H. Zhou. "Spectral approximation by the polar transformation." Canadian Journal of Physics 76, no. 1 (January 1, 1998): 31–37. http://dx.doi.org/10.1139/p97-047.

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Central potentials V(r) are considered that admit the polar representation V(r) = g(h(r)), where h(r) = sgn (q)rq, q is fixed, and g is the polar transformation function. This representation allows the Schrödinger eigenvalues generated by V to be approximated in terms of those generated by the pure polar potential h(r). In many cases a pair of powers {q1, q2} can be chosen so that the corresponding polar functions {g1, g2} have definite and opposite convexity. For such cases, the spectral approximations provide both upper and lower bounds for the entire discrete spectrum. The example V(r) = ar2 + br2/(1 + cr2) is considered in detail. PACS No. 03.65Ge

26

Mateljevic, Miodrag, Marek Svetlik, Miloljub Albijanic, and Nebojsa Savic. "Generalizations of the Lagrange mean value theorem and applications." Filomat 27, no. 4 (2013): 515–28. http://dx.doi.org/10.2298/fil1304515m.

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In this paper we give a generalization of the Lagrange mean value theorem via lower and upper derivative, as well as appropriate criteria of monotonicity and convexity for arbitrary function f : (a, b) ( R. Some applications to the neoclassical economic growth model are given (from mathematical point of view).

27

Milton, Graeme W. "Addendum to ‘Sharp inequalities that generalize the divergence theorem: an extension of the notion of quasi-convexity’." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2176 (April 2015): 20140886. http://dx.doi.org/10.1098/rspa.2014.0886.

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The paper ‘Sharp inequalities that generalize the divergence theorem: an extension of the notion of quasi-convexity’ published in Proc. R. Soc. A 2013, 469, 20130075 ( doi:10.1098/rspa.2013.0075 ) is clarified. Notably, much more general boundary conditions are given under which sharp lower bounds on the integrals of certain quadratic functions of the fields can be obtained. More precisely, if the quadratic form is Q *-convex then any solution of the Euler–Lagrange equations will necessarily minimize the integral. As a consequence, strict Q *-convexity is found to be an appropriate condition to ensure uniqueness of the solutions of a wide class of linear Euler–Lagrange equations in a given domain Ω with appropriate boundary conditions.

28

Aydi, Hassen, Bessem Samet, and Manuel De la Sen. "A generalization of convexity via an implicit inequality." AIMS Mathematics 9, no. 5 (2024): 11992–2010. http://dx.doi.org/10.3934/math.2024586.

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<abstract><p>We unified several kinds of convexity by introducing the class $ \mathcal{A}_{\zeta, w}([0, 1]\times I^2) $ of $ (\zeta, w) $-admissible functions $ F: [0, 1]\times I\times I\to \mathbb{R} $. Namely, we proved that most types of convexity from the literature generate functions $ F\in \mathcal{A}_{\zeta, w}([0, 1]\times I^2) $ for some $ \zeta\in C([0, 1]) $ and $ w\in C^1(I) $ with $ w(I)\subset I $ and $ w' > 0 $. We also studied some properties of $ (\zeta, w) $-admissible functions and established some integral inequalities that unify various Hermite-Hadamard-type inequalities from the literature.</p></abstract>

29

El Hajj, L., and H. Shahgholian. "Remarks on the convexity of free boundaries (Scalar and system cases)." St. Petersburg Mathematical Journal 32, no. 4 (July 9, 2021): 713–27. http://dx.doi.org/10.1090/spmj/1666.

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Convexity is discussed for several free boundary value problems in exterior domains that are generally formulated as Δ u = f ( u ) in Ω ∖ D , | ∇ u | = g on ∂ Ω , u ≥ 0 in R n , \begin{equation*} \Delta u = f(u) \ \text {in } \Omega \setminus D, \quad |\nabla u | = g \ \text { on } \ \partial \Omega , \quad u\geq 0 \ \text { in } \ \mathbb {R}^n, \end{equation*} where u u is assumed to be continuous in R n \mathbb {R}^n , Ω = { u > 0 } \Omega = \{u > 0\} (is unknown), u = 1 u=1 on ∂ D \partial D , and D D is a bounded domain in R n \mathbb {R}^n ( n ≥ 2 n\geq 2 ). Here g = g ( x ) g= g(x) is a given smooth function that is either strictly positive (Bernoulli-type) or identically zero (obstacle type). Properties for f f will be spelled out in exact terms in the text. The interest is in the particular case where D D is star-shaped or convex. The focus is on the case where f ( u ) f(u) lacks monotonicity, so that the recently developed tool of quasiconvex rearrangement is not applicable directly. Nevertheless, such quasiconvexity is used in a slightly different manner, and in combination with scaling and asymptotic expansion of solutions at regular points. The latter heavily relies on the regularity theory of free boundaries. Also, convexity for several systems of equations in a general framework is discussed, and some ideas along with several open problems are presented.

30

Ahmad, H., R. B. Khokhar, M. Suleman, M. Tariq, S. K. Ntouyas, and J. Tariboon. "Some new notions of fractional Hermite-Hadamard type inequalities involving applications to the physical sciences." Journal of Mathematics and Computer Science 33, no. 01 (November 16, 2023): 27–41. http://dx.doi.org/10.22436/jmcs.033.01.03.

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The term convexity in the frame of fractional calculus is a well-established concept that has assembled significant attention in mathematics and various scientific disciplines for over a century. It offers valuable insights and results in diverse fields, along with practical applications due to its geometric interpretation. Moreover, convexity provides researchers with powerful tools and numerical methods for addressing extensive interconnected problems. In the realm of applied mathematics, convexity, particularly in relation to fractional analysis, finds extensive and remarkable applications. In this manuscript, we construct new fractional identities for differentiable preinvex functions to strengthen the recently assigned approach even more. Then utilizing these identities, some generalizations of the Hermite-Hadamard type inequality involving generalized preinvexities in the frame of fractional integral operator, namely Riemann-Liouville (R-L) fractional integrals are explored. Finally, we examined some applications to the q -digamma and Bessel functions via the established results. We used fundamental methods to arrive at our conclusions. We anticipate the techniques and approaches addressed by this study will further pique and spark the researcher's interest.

31

Pavic, Zlatko. "The Fejér inequality and its generalizations." Filomat 32, no. 16 (2018): 5793–802. http://dx.doi.org/10.2298/fil1816793p.

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The article provides generalizations of the Fej?r inequality. These include extensions, and refinements by inserting discrete and integral terms. The fundamental issue underlying this research is the barycenter of a nonnegative integrable function. Appropriate properties of the convexity related to the function barycenter are used in the construction of main results.

32

Oros, Georgia Irina. "New Conditions for Univalence of Confluent Hypergeometric Function." Symmetry 13, no. 1 (January 5, 2021): 82. http://dx.doi.org/10.3390/sym13010082.

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Since in many particular cases checking directly the conditions from the definitions of starlikeness or convexity of a function can be difficult, in this paper we use the theory of differential subordination and in particular the method of admissible functions in order to determine conditions of starlikeness and convexity for the confluent (Kummer) hypergeometric function of the first kind. Having in mind the results obtained by Miller and Mocanu in 1990 who used a,c∈R, for the confluent (Kummer) hypergeometric function, in this investigation a and c complex numbers are used and two criteria for univalence of the investigated function are stated. An example is also included in order to show the relevance of the original results of the paper.

33

Li, Wenbo V., and Vladislav V. Vysotsky. "Probabilities of Competing Binomial Random Variables." Journal of Applied Probability 49, no. 3 (September 2012): 731–44. http://dx.doi.org/10.1239/jap/1346955330.

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Suppose that both you and your friend toss an unfair coin n times, for which the probability of heads is equal to α. What is the probability that you obtain at least d more heads than your friend if you make r additional tosses? We obtain asymptotic and monotonicity/convexity properties for this competing probability as a function of n, and demonstrate surprising phase transition phenomenon as the parameters d, r, and α vary. Our main tools are integral representations based on Fourier analysis.

34

BARBOSU, DAN. "On the approximation of convex functions using linear positive operators." Creative Mathematics and Informatics 26, no. 2 (2017): 137–43. http://dx.doi.org/10.37193/cmi.2017.02.03.

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The goal of the paper is to present some results concerning the approximation of convex functions by linear positive operators. First, one recalls some results concerning the univariate real valued convex functions. Next, one presents the notion of higher order convexity introduced by Popoviciu [Popoviciu, T., Sur quelques propri´et´ees des fonctions d’une ou deux variable r´eelles, PhD Thesis, La Faculte des Sciences de Paris, 1933 (June)]. The Popoviciu’s famous theorem for the representation of linear functionals associated to convex functions of m−th order (with the proof of author) is also presented. Finally, applications of the convexity to study the monotonicity of sequences of some linear positive operators and also mean value theorems for the remainder term of some approximation formulas based on linear positive operators are presented.

35

Imtiaz, Annam, and Ch Rehan Qamar. "Facial Profile Convexity in Skeletal Class II Malocclusion: How Soft Tissue Angle of Facial Convexity (SA-FC) Correlate with Angle ANB in Skeletal Class II Subjects." Journal of the Pakistan Dental Association 31, no. 02 (July 17, 2022): 86–90. http://dx.doi.org/10.25301/jpda.312.86.

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OBJECTIVE: The research was conducted to determine the correlation between Soft tissue angle of facial convexity (SA-FC) and angle ANB in skeletal class II malocclusion. The outcome of the study will help in determining if the routine consideration of ANB angle while the lack of defined thresholds for convexity of soft tissue profile justified for choosing the treatment modality. METHODOLOGY: Lateral cephalograms of 141 skeletal class II subjects (ANB>4°) were obtained. Angular parameters including soft tissue angle of facial convexity (SA-FC) and angle ANB were determined. Gender dimorphism of the variables was assessed by Mann Whitney U test. Correlation between SA-FC and angle ANB were determined utilizing Spearman's correlation coefficient. RESULTS: The angle SA-FC and ANB depicted moderately positive correlation (r = 0.662, p<0.001). Gender dimorphism exists with increased mean value of ANB (7.88±1.90) and SA-FC (23.22±7.61) in females. CONCLUSIONS: Angle SA-FC depicts moderately positive correlation with angle ANB among skeletal class II subjects, hence suggesting the need of soft tissue guidelines along-with hard tissue parameters for selection of treatment modality. KEYWORDS: Cephalometry, Malocclusion, Diagnosis, soft tissue, correlation.

36

Mulyava, O. M., M. M. Sheremeta, and Yu S. Trukhan. "Properties of solutions of a heterogeneous differential equation of the second order." Carpathian Mathematical Publications 11, no. 2 (December 31, 2019): 379–98. http://dx.doi.org/10.15330/cmp.11.2.379-398.

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Suppose that a power series $A(z)=\sum_{n=0}^{\infty}a_n z^{n}$ has the radius of convergence $R[A]\in [1,+\infty]$. For a heterogeneous differential equation $$ z^2 w''+(\beta_0 z^2+\beta_1 z) w'+(\gamma_0 z^2+\gamma_1 z+\gamma_2)w=A(z) $$ with complex parameters geometrical properties of its solutions (convexity, starlikeness and close-to-convexity) in the unit disk are investigated. Two cases are considered: if $\gamma_2\neq0$ and $\gamma_2=0$. We also consider cases when parameters of the equation are real numbers. Also we prove that for a solution $f$ of this equation the radius of convergence $R[f]$ equals to $R[A]$ and the recurrent formulas for the coefficients of the power series of $f(z)$ are found. For entire solutions it is proved that the order of a solution $f$ is not less then the order of $A$ ($\varrho[f]\ge\varrho[A]$) and the estimate is sharp. The same inequality holds for generalized orders ($\varrho_{\alpha\beta}[f]\ge \varrho_{\alpha\beta}[A]$). For entire solutions of this equation the belonging to convergence classes is studied. Finally, we consider a linear differential equation of the endless order $ \sum\limits_{n=0}^{\infty}\dfrac{a_n}{n!}w^{(n)}=\Phi(z), $ and study a possible growth of its solutions.

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Latif, Muhammad, Sever Dragomir, and Ebrahim Momoniat. "Some Fejér type integral inequalities for geometrically-arithmetically-convex functions with applications." Filomat 32, no. 6 (2018): 2193–206. http://dx.doi.org/10.2298/fil1806193l.

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In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving geometrically symmetric functions is established, and by using the obtained identity, the H?lder integral inequality and the notion of geometrically-arithmetically convexity, some new Fej?r type integral inequalities are presented. Applications of our results to special means of positive real numbers are given as well.

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Alb Lupaş, Alina. "Properties on a subclass of univalent functions defined by using a multiplier transformation and Ruscheweyh derivative." Analele Universitatii "Ovidius" Constanta - Seria Matematica 23, no. 1 (January 1, 2015): 9–24. http://dx.doi.org/10.1515/auom-2015-0001.

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AbstractIn this paper we have introduced and studied the subclass ℛ𝒥 (d, α, β) of univalent functions defined by the linear operator $RI_{n,\lambda ,l}^\gamma f(z)$ defined by using the Ruscheweyh derivative Rnf(z) and multiplier transformation I (n, λ, l) f(z), as $RI_{n,\lambda ,l}^\gamma :{\cal A} \to {\cal A}$, $RI_{n,\lambda ,l}^\gamma f(z) = (1 - \gamma )R^n f(z) + \gamma I(n,\lambda ,l)f(z)$, z ∈ U, where 𝒜n ={f ∈ ℋ(U) : f(z) = z + an+1zn+1 + . . . , z ∈ U}is the class of normalized analytic functions with 𝒜1 = 𝒜. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class ℛ𝒥(d, α, β).

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Safaei, Nozar, and Ali Barani. "SCHUR-CONVEXITY OF INTEGRAL ARITHMETIC MEANS OF CO-ORDINATED CONVEX FUNCTIONS IN `R^3`." Mathematical Analysis and Convex Optimization 1, no. 1 (February 1, 2020): 0. http://dx.doi.org/10.29252/maco.1.1.3.

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Zhang, Hongtao. "A Note on the Convexity of Service-Level Measures of the (r, q) System." Management Science 44, no. 3 (March 1998): 431–32. http://dx.doi.org/10.1287/mnsc.44.3.431.

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Kodamasingh, Bibhakar, Soubhagya Kumar Sahoo, Wajid Ali Shaikh, Kamsing Nonlaopon, Sotiris K. Ntouyas, and Muhammad Tariq. "Some New Integral Inequalities Involving Fractional Operator with Applications to Probability Density Functions and Special Means." Axioms 11, no. 11 (October 29, 2022): 602. http://dx.doi.org/10.3390/axioms11110602.

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Fractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer order. Lately, it has attracted the attention of several mathematicians because of its real-life applications. More importantly, it has turned into a valuable tool for handling elements from perplexing frameworks within different parts of the pure and applied sciences. Integral inequalities, in association with convexity, have a strong relationship with symmetry. The objective of this article is to introduce the notion of operator refined exponential type convexity. Fractional versions of the Hermite–Hadamard type inequality employing generalized R−L fractional operators are established. Additionally, some novel refinements of Hermite–Hadamard type inequalities are also discussed using some established identities. Finally, we present some applications of the probability density function and special means of real numbers.

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Tassaddiq, Asifa, Muhammad Tanveer, Khuram Israr, Muhammad Arshad, Khurrem Shehzad, and Rekha Srivastava. "Multicorn Sets of z¯k+cm via S-Iteration with h-Convexity." Fractal and Fractional 7, no. 6 (June 18, 2023): 486. http://dx.doi.org/10.3390/fractalfract7060486.

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Fractals represent important features of our natural environment, and therefore, several scientific fields have recently begun using fractals that employ fixed-point theory. While many researchers are working on fractals (i.e., Mandelbrot and Julia sets), only a very few have focused on multicorn sets and their dynamic nature. In this paper, we study the dynamics of multicorn sets of z¯k+cm, where k≥2, c≠0∈C, and m∈R, by using S-iteration with h-convexity instead of standard S-iteration. We develop escape criterion z¯k+cm for S-iteration with h-convexity. We analyse the dynamical behaviour of the proposed conjugate complex function and discuss the variation of iteration parameters along with function parameter m. Moreover, we discuss the effects of input parameters of the proposed iteration and conjugate complex functions of the behaviour of multicorn sets with numerical simulations.

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Hershkovits, Or. "Translators asymptotic to cylinders." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 766 (September 1, 2020): 61–71. http://dx.doi.org/10.1515/crelle-2019-0023.

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AbstractWe show that the Bowl soliton in {\mathbb{R}^{3}} is the unique translating solution of the mean curvature flow whose tangent flow at {-\infty} is the shrinking cylinder. As an application, we show that for a generic mean curvature flow, all (non-static) translating limit flows are the bowl soliton. The crucial point is that we do not make any global convexity assumption, while as the same time, the asymptotic requirement is very weak.

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Hernandez, Francisco L., and Nigel J. Kalton. "Subspaces of Rearrangement-Invariant Spaces." Canadian Journal of Mathematics 48, no. 4 (August 1, 1996): 794–833. http://dx.doi.org/10.4153/cjm-1996-041-4.

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AbstractWe prove a number of results concerning the embedding of a Banach lattice X into an r. i. space Y. For example we show that if Y is an r. i. space on [0, ∞) which is p-convex for some p > 2 and has nontrivial concavity then any Banach lattice X which is r-convex for some r > 2 and embeds into Y must embed as a sublattice. Similar conclusions can be drawn under a variety of hypotheses on Y; if X is an r. i. space on [0, 1] one can replace the hypotheses of r-convexity for some r > 2 by X ≠ L2.We also show that if Y is an order-continuous Banach lattice which contains no complemented sublattice lattice-isomorphic to ℓ2X is an order-continuous Banach lattice so that ℓ2 is not complementary lattice finitely representable in X and X is isomorphic to a complemented subspace of Y then X is isomorphic to a complemented sublattice of YN for some integer N.

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Li, Wenbo V., and Vladislav V. Vysotsky. "Probabilities of Competing Binomial Random Variables." Journal of Applied Probability 49, no. 03 (September 2012): 731–44. http://dx.doi.org/10.1017/s0021900200009505.

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Suppose that both you and your friend toss an unfair coinntimes, for which the probability of heads is equal to α. What is the probability that you obtain at leastdmore heads than your friend if you makeradditional tosses? We obtain asymptotic and monotonicity/convexity properties for this competing probability as a function ofn, and demonstrate surprising phase transition phenomenon as the parametersd,r, and α vary. Our main tools are integral representations based on Fourier analysis.

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Shilpa, N., and Irawati S Latha. "ON SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING q-DERIVATIVE OPERATOR WITH NEGATIVE COEFFICIENTS." South East Asian J. of Mathematics and Mathematical Sciences 19, no. 03 (December 30, 2023): 37–48. http://dx.doi.org/10.56827/seajmms.2023.1903.4.

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The purpose of this work is to introduce and study new subclasses of analytic functions using a new q-derivative operator. This operator generalizes the operators introduced by Al-Oboudi, Catas, Cho and Kim, Cho and Srivastava, Maslina Darus and R W Ibrahim, Sˇalˇagean, Uralegaddi and Somanatha. We investigate coefficient bounds, growth, distortion and closure theorems for the functions belonging to these classes. We also give a result which unifies radii of close-toconvexity, starlikeness and convexity.

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Hough, C. L., and Y. Chang. "Constrained Cutting Rate-Tool Life Characteristic Curve, Part 1: Theory and General Case." Journal of Manufacturing Science and Engineering 120, no. 1 (February 1, 1998): 156–59. http://dx.doi.org/10.1115/1.2830092.

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The concept of a cutting rate-tool life (R-T) characteristic curve is extended to the general machining economics problem (MEP) with a quadratic-logarithmic tool life and constraint equations. The R-T characteristic curve presents the general loci of optima, which is useful in selecting optimal parameters for multiple machining conditions. The necessary and sufficient conditions for the global optimum of the unconstrained MEP are presented. These conditions are equivalently applied to the concept of the constrained R-T characteristic curve. In terms of quadratic geometric programming the objective function and constraints of the general MEP are called as quadratic posylognomials (QPL). The QPL problems are classified as convex and nonconvex and the convexity is determined by the second order terms of the tool life model. Nonlinear programming and an exhaustive method are demonstrated to determine the R-T characteristic curve for three cases of posynomial, convex QPL, and non-convex QPL problems.

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JOHNSON, WILLIAM B., JORAM LINDENSTRAUSS, DAVID PREISS, and GIDEON SCHECHTMAN. "ALMOST FRÉCHET DIFFERENTIABILITY OF LIPSCHITZ MAPPINGS BETWEEN INFINITE-DIMENSIONAL BANACH SPACES." Proceedings of the London Mathematical Society 84, no. 3 (April 29, 2002): 711–46. http://dx.doi.org/10.1112/s0024611502013400.

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We give several sufficient conditions on a pair of Banach spaces X and Y under which each Lipschitz mapping from a domain in X to Y has, for every $\epsilon > 0$, a point of $\epsilon$-Fréchet differentiability. Most of these conditions are stated in terms of the moduli of asymptotic smoothness and convexity, notions which have appeared in the literature under a variety of names. We prove, for example, that for $\infty > r > p \ge 1$, every Lipschitz mapping from a domain in an $\ell_r$-sum of finite-dimensional spaces into an $\ell_p$-sum of finite-dimensional spaces has, for every $\epsilon > 0$, a point of $\epsilon$-Fréchet differentiability, and that every Lipschitz mapping from an asymptotically uniformly smooth space to a finite-dimensional space has such points. The latter result improves, with a simpler proof, an earlier result of the second and third authors. We also survey some of the known results on the notions of asymptotic smoothness and convexity, prove some new properties, and present some new proofs of existing results.2000 Mathematical Subject Classification: 46G05, 46T20.

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Katzourakis, Nikos. "Solutions of vectorial Hamilton–Jacobi equations are rank-one absolute minimisers in L ∞ L^{\infty}." Advances in Nonlinear Analysis 8, no. 1 (June 4, 2017): 508–16. http://dx.doi.org/10.1515/anona-2016-0164.

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Abstract Given the supremal functional {E_{\infty}(u,\Omega^{\prime})=\operatornamewithlimits{ess\,sup}_{\Omega^{% \prime}}H(\,\cdot\,,\mathrm{D}u)} , defined on {W^{1,\infty}_{\mathrm{loc}}(\Omega,\mathbb{R}^{N})} , with {\Omega^{\prime}\Subset\Omega\subseteq\mathbb{R}^{n}} , we identify a class of vectorial rank-one absolute minimisers by proving a statement slightly stronger than the next claim: vectorial solutions of the Hamilton–Jacobi equation {H(\,\cdot\,,\mathrm{D}u)=c} are rank-one absolute minimisers if they are {C^{1}} . Our minimality notion is a generalisation of the classical {L^{\infty}} variational principle of Aronsson to the vector case, and emerged in earlier work of the author. The assumptions are minimal, requiring only continuity and rank-one convexity of the level sets.

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Anh, V. V., and P. D. Tuan. "Extremal problems for a class of functions of positive real part and applications." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 2 (October 1986): 152–64. http://dx.doi.org/10.1017/s1446788700033577.

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AbstractIn this paper we determine the lower bound on |z| = r < 1 for the functional Re{αp(z) + β zp′(z)/p(z)}, α ≧0, β ≧ 0, over the class Pk (A, B). By means of this result, sharp bounds for |F(z)|, |F',(z)| in the family and the radius of convexity for are obtained. Furthermore, we establish the radius of starlikness of order β, 0 ≦ β < 1, for the functions F(z) = λf(Z) + (1-λ) zf′ (Z), |z| < 1, where ∞ < λ <1, and .