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Journal articles on the topic 'Geometric-analytic inequalities'

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Author: Grafiati
Published: 10 March 2023

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1

Ku, Hsu-Tung, Mei-Chin Ku, and Xin-Min Zhang. "Analytic and geometric isoperimetric inequalities." Journal of Geometry 53, no. 1-2 (July 1995): 100–121. http://dx.doi.org/10.1007/bf01224044.

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2

Brooks, Robert. "Book Review: Isoperimetric inequalities: Differential geometric and analytic perspectives." Bulletin of the American Mathematical Society 39, no. 04 (July 10, 2002): 581–85. http://dx.doi.org/10.1090/s0273-0979-02-00954-0.

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3

Venkateswarlu, Bolenini, Pinninti Thirupathi Reddy, Şahsene Altınkaya, Nattakan Boonsatit, Porpattama Hammachukiattikul, and Vaishnavy Sujatha. "On a Certain Subclass of Analytic Functions Defined by Touchard Polynomials." Symmetry 14, no. 4 (April 18, 2022): 838. http://dx.doi.org/10.3390/sym14040838.

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This paper focuses on the establishment of a new subfamily of analytic functions including Touchard polynomials. Then, we attempt to obtain geometric properties such as coefficient inequalities, distortion properties, extreme points, radii of starlikeness and convexity, partial sums, neighbourhood results and integral means’ inequality for this class. The symmetry properties of the subfamily of functions established in the current paper may be examined as future research directions.
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4

Al-shbeil, Isra, Jianhua Gong, and Timilehin Gideon Shaba. "Coefficients Inequalities for the Bi-Univalent Functions Related to q-Babalola Convolution Operator." Fractal and Fractional 7, no. 2 (February 4, 2023): 155. http://dx.doi.org/10.3390/fractalfract7020155.

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This article defines a new operator called the q-Babalola convolution operator by using quantum calculus and the convolution of normalized analytic functions in the open unit disk. We then study a new class of analytic and bi-univalent functions defined in the open unit disk associated with the q-Babalola convolution operator. The main results of the investigation include some upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szego inequalities for the functions in the new class. Many applications of the finds are highlighted in the corollaries based on the various unique choices of the parameters, improving the existing results in Geometric Function Theory.
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5

Ibrahim, Rabha W., Rafida M. Elobaid, and Suzan J. Obaiys. "Geometric Inequalities via a Symmetric Differential Operator Defined by Quantum Calculus in the Open Unit Disk." Journal of Function Spaces 2020 (August 18, 2020): 1–8. http://dx.doi.org/10.1155/2020/6932739.

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The present investigation covenants with the concept of quantum calculus besides the convolution operation to impose a comprehensive symmetric q-differential operator defining new classes of analytic functions. We study the geometric representations with applications. The applications deliberated to indicate the certainty of resolutions of a category of symmetric differential equations type Briot-Bouquet.
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6

Singh, Gagandeep, and Gurcharanjit Singh. "COEFFICIENT PROBLEMS FOR THE SUBCLASSES OF SAKAGUCHI TYPE FUNCTIONS ASSOCIATED WITH SINE FUNCTION." Jnanabha 51, no. 02 (2021): 237–43. http://dx.doi.org/10.58250/jnanabha.2021.51230.

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Abstract The estimation of the upper bound for certain coefficient relations of various subclasses of analytic functions is an active topic of research in Geometric function theory. In this paper, certain subclasses of Sakaguchi type functions are defined by subordinating to sine function in the open unit disc E = {z : |z| < 1} and some coefficient inequalities such as Fekete-Szegö inequality, Second Hankel determinant, Zalcman functional and third Hankel determinant are investigated.
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7

Aldawish, Ibtisam, Rabha W. Ibrahim, and Suzan J. Obaiys. "A Class of Symmetric Fractional Differential Operator Formed by Special Functions." Journal of Mathematics 2022 (August 2, 2022): 1–10. http://dx.doi.org/10.1155/2022/8339837.

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In light of a certain sort of fractional calculus, a generalized symmetric fractional differential operator based on Raina’s function is built. The generalized operator is then used to create a formula for analytic functions of type normalized. We use the ideas of subordination and superordination to show a collection of inequalities using the suggested differential operator. The new Raina’s operator is also used to the generalized kinematic solutions (GKS). Using the concepts of subordination and superordination, we provide analytic solutions for GKS. As a consequence, a certain hypergeometric function provides the answer. A fractional coefficient differential operator is also created. The geometric and analytic properties of the object are being addressed. The symmetric differential operator in a complex domain is shown to be a generalized fractional differential operator. Finally, we explore the characteristics of the Raina’s symmetric differential operator.
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8

SONG, ZHIGANG, J. Q. LIANG, and L. F. WEI. "SPIN-PARITY EFFECT IN VIOLATION OF BELL'S INEQUALITIES." Modern Physics Letters B 28, no. 01 (December 23, 2013): 1450004. http://dx.doi.org/10.1142/s0217984914500043.

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Analytic formulas of Bell correlations are derived in terms of quantum probability statistics under the assumption of measuring outcome-independence and the Bell's inequalities (BIs) are extended to general bipartite-entanglement macroscopic quantum-states (MQS) of arbitrary spins. For a spin-½ entangled state we find analytically that the violations of BIs really resulted from the quantum nonlocal correlations. However, the BIs are always satisfied for the spin-1 entangled MQS. More generally the quantum nonlocality does not lead to the violation for the integer spins since the nonlocal interference effects cancel each other by the quantum statistical-average. Such a cancellation no longer exists for the half-integer spins due to the nontrivial Berry phase, and thus the violation of BIs is understood remarkably as an effect of geometric phase. Specifically, our generic observation of the spin-parity effect can be experimentally tested with the entangled photon-pairs.
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9

Aldawish, Ibtisam, and Rabha W. Ibrahim. "Solvability of a New q-Differential Equation Related to q-Differential Inequality of a Special Type of Analytic Functions." Fractal and Fractional 5, no. 4 (November 17, 2021): 228. http://dx.doi.org/10.3390/fractalfract5040228.

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The current study acts on the notion of quantum calculus together with a symmetric differential operator joining a special class of meromorphic multivalent functions in the puncher unit disk. We formulate a quantum symmetric differential operator and employ it to investigate the geometric properties of a class of meromorphic multivalent functions. We illustrate a set of differential inequalities based on the theory of subordination and superordination. In this real case study, we found the analytic solutions of q-differential equations. We indicate that the solutions are given in terms of confluent hypergeometric function of the second type and Laguerre polynomial.
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10

Feehan, Paul M. N., and Manousos Maridakis. "Łojasiewicz–Simon gradient inequalities for analytic and Morse–Bott functions on Banach spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 765 (August 1, 2020): 35–67. http://dx.doi.org/10.1515/crelle-2019-0029.

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AbstractWe prove several abstract versions of the Łojasiewicz–Simon gradient inequality for an analytic function on a Banach space that generalize previous abstract versions of this inequality, weakening their hypotheses and, in particular, that of the well-known infinite-dimensional version of the gradient inequality due to Łojasiewicz [S. Łojasiewicz, Ensembles semi-analytiques, (1965), Publ. Inst. Hautes Etudes Sci., Bures-sur-Yvette. LaTeX version by M. Coste, August 29, 2006 based on mimeographed course notes by S. Łojasiewicz, https://perso.univ-rennes1.fr/michel.coste/Lojasiewicz.pdf] and proved by Simon [L. Simon, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math. (2) 118 1983, 3, 525–571]. We prove that the optimal exponent of the Łojasiewicz–Simon gradient inequality is obtained when the function is Morse–Bott, improving on similar results due to Chill [R. Chill, On the Łojasiewicz–Simon gradient inequality, J. Funct. Anal. 201 2003, 2, 572–601], [R. Chill, The Łojasiewicz–Simon gradient inequality in Hilbert spaces, Proceedings of the 5th European-Maghrebian workshop on semigroup theory, evolution equations, and applications 2006, 25–36], Haraux and Jendoubi [A. Haraux and M. A. Jendoubi, On the convergence of global and bounded solutions of some evolution equations, J. Evol. Equ. 7 2007, 3, 449–470], and Simon [L. Simon, Theorems on regularity and singularity of energy minimizing maps, Lect. Math. ETH Zürich, Birkhäuser, Basel 1996]. In [P. M. N. Feehan and M. Maridakis, Łojasiewicz–Simon gradient inequalities for harmonic maps, preprint 2019, https://arxiv.org/abs/1903.01953], we apply our abstract gradient inequalities to prove Łojasiewicz–Simon gradient inequalities for the harmonic map energy function using Sobolev spaces which impose minimal regularity requirements on maps between closed, Riemannian manifolds. Those inequalities generalize those of Kwon [H. Kwon, Asymptotic convergence of harmonic map heat flow, ProQuest LLC, Ann Arbor 2002; Ph.D. thesis, Stanford University, 2002], Liu and Yang [Q. Liu and Y. Yang, Rigidity of the harmonic map heat flow from the sphere to compact Kähler manifolds, Ark. Mat. 48 2010, 1, 121–130], Simon [L. Simon, Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems, Ann. of Math. (2) 118 1983, 3, 525–571], [L. Simon, Isolated singularities of extrema of geometric variational problems, Harmonic mappings and minimal immersions (Montecatini 1984), Lecture Notes in Math. 1161, Springer, Berlin 1985, 206–277], and Topping [P. M. Topping, Rigidity in the harmonic map heat flow, J. Differential Geom. 45 1997, 3, 593–610]. In [P. M. N. Feehan and M. Maridakis, Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions, preprint 2019, https://arxiv.org/abs/1510.03815v6; to appear in Mem. Amer. Math. Soc.], we prove Łojasiewicz–Simon gradient inequalities for coupled Yang–Mills energy functions using Sobolev spaces which impose minimal regularity requirements on pairs of connections and sections. Those inequalities generalize that of the pure Yang–Mills energy function due to the first author [P. M. N. Feehan, Global existence and convergence of solutions to gradient systems and applications to Yang–Mills gradient flow, preprint 2016, https://arxiv.org/abs/1409.1525v4] for base manifolds of arbitrary dimension and due to Råde [J. Råde, On the Yang–Mills heat equation in two and three dimensions, J. reine angew. Math. 431 1992, 123–163] for dimensions two and three.
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11

Saliu, Afis, Isra Al-Shbeil, Jianhua Gong, Sarfraz Nawaz Malik, and Najla Aloraini. "Properties of q-Symmetric Starlike Functions of Janowski Type." Symmetry 14, no. 9 (September 12, 2022): 1907. http://dx.doi.org/10.3390/sym14091907.

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The word “symmetry” is a Greek word that originated from “symmetria”. It means an agreement in dimensions, due proportion, and arrangement; however, in complex analysis, it means objects remaining invariant under some transformation. This idea has now been recently used in geometric function theory to modify the earlier classical q-derivative introduced by Ismail et al. due to its better convergence properties. Consequently, we introduce a new class of analytic functions by using the notion of q-symmetric derivative. The investigation in this paper obtains a number of the latest important results in q-theory, including coefficient inequalities and convolution characterization of q-symmetric starlike functions related to Janowski mappings.
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12

Ibrahim, Rabha W., and Maslina Darus. "New Symmetric Differential and Integral Operators Defined in the Complex Domain." Symmetry 11, no. 7 (July 12, 2019): 906. http://dx.doi.org/10.3390/sym11070906.

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The symmetric differential operator is a generalization operating of the well-known ordinary derivative. These operators have advantages in boundary value problems, statistical studies and spectral theory. In this effort, we introduce a new symmetric differential operator (SDO) and its integral in the open unit disk. This operator is a generalization of the Sàlàgean differential operator. Our study is based on geometric function theory and its applications in the open unit disk. We formulate new classes of analytic functions using SDO depending on the symmetry properties. Moreover, we define a linear combination operator containing SDO and the Ruscheweyh derivative. We illustrate some inclusion properties and other inequalities involving SDO and its integral.
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13

Bounkhel, Messaoud. "Calculus Rules forV-Proximal Subdifferentials in Smooth Banach Spaces." Journal of Function Spaces 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/1917387.

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In 2010, Bounkhel et al. introduced new proximal concepts (analytic proximal subdifferential, geometric proximal subdifferential, and proximal normal cone) in reflexive smooth Banach spaces. They proved, inp-uniformly convex andq-uniformly smooth Banach spaces, the density theorem for the new concepts of proximal subdifferential and various important properties for both proximal subdifferential concepts and the proximal normal cone concept. In this paper, we establish calculus rules (fuzzy sum rule and chain rule) for both proximal subdifferentials and we prove the Bishop-Phelps theorem for the proximal normal cone. The limiting concept for both proximal subdifferentials and for the proximal normal cone is defined and studied. We prove that both limiting constructions coincide with the Mordukhovich constructions under some assumptions on the space. Applications to nonconvex minimisation problems and nonconvex variational inequalities are established.
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14

Alarifi, Najla M., and Rabha W. Ibrahim. "Specific Classes of Analytic Functions Communicated with a Q-Differential Operator Including a Generalized Hypergeometic Function." Fractal and Fractional 6, no. 10 (September 27, 2022): 545. http://dx.doi.org/10.3390/fractalfract6100545.

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A special function is a function that is typically entitled after an early scientist who studied its features and has a specific application in mathematical physics or another area of mathematics. There are a few significant examples, including the hypergeometric function and its unique species. These types of special functions are generalized by fractional calculus, fractal, q-calculus, (q,p)-calculus and k-calculus. By engaging the notion of q-fractional calculus (QFC), we investigate the geometric properties of the generalized Prabhakar fractional differential operator in the open unit disk ∇:={ξ∈C:|ξ|<1}. Consequently, we insert the generalized operator in a special class of analytic functions. Our methodology is indicated by the usage of differential subordination and superordination theory. Accordingly, numerous fractional differential inequalities are organized. Additionally, as an application, we study the solution of special kinds of q–fractional differential equation.
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15

Al-Khafaji, Thamer Khalil MS, and Asmaa KH Abdul-Rahman. "Derivative Operator of Order ε+ρ-1 Associated with Differential Subordination and Superordination." Mathematical Modelling of Engineering Problems 9, no. 2 (April 28, 2022): 431–36. http://dx.doi.org/10.18280/mmep.090218.

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Professors Miller and Mocanu established the theory of differential subordination and its twin, the theory of differential super ordination, which are both based on reinterpreting fundamental inequalities for real-valued functions for the situation of complex-valued functions. Using different types of operators to study subordination and super ordination characteristics is a technique that is still extensively employed, with some investigations leading to sandwich-type theorems, as is the case in the current work. The objective of this work is to derive differential Subordination and Super ordination outcomes using the derivative operator of order E+-1. Differential subordination and super ordination results are achieved for analytic functions connected with the integral operator in the open unit disc. These findings are achieved by examining relevant types of admissible functions, differential supremacy theorem, several operator differential hyperboloids requiring partial integration of a stacking suprageometric function are produced, as well as the best subordinates. The result of a sandwich type links the outcomes of dependency and dependency using Theorem 9. Keep track of intriguing corollaries for certain occupations by using the best subordinate and dominant skills. Presented in this paper may be used to motivate the usage of alternative hyper-geometric functions related to partial integration.
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16

Grigor'yan, Alexander. "ISOPERIMETRIC INEQUALITIES: DIFFERENTIAL GEOMETRIC AND ANALYTIC PERSPECTIVES (Cambridge Tracts in Mathematics 145) By ISAAC CHAVEL: 268 pp., £50.00, ISBN 0-521-80267-9 (Cambridge University Press, 2001)." Bulletin of the London Mathematical Society 34, no. 05 (September 2002): 619–31. http://dx.doi.org/10.1112/s0024609302211376.

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17

Alarifi, Najla M., and Rabha W. Ibrahim. "Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable." Journal of Function Spaces 2021 (September 10, 2021): 1–11. http://dx.doi.org/10.1155/2021/4797955.

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Saint-Venant equations describe the flow below a pressure surface in a fluid. We aim to generalize this class of equations using fractional calculus of a complex variable. We deal with a fractional integral operator type Prabhakar operator in the open unit disk. We formulate the extended operator in a linear convolution operator with a normalized function to study some important geometric behaviors. A class of integral inequalities is investigated involving special functions. The upper bound of the suggested operator is computed by using the Fox-Wright function, for a class of convex functions and univalent functions. Moreover, as an application, we determine the upper bound of the generalized fractional 2-dimensional Saint-Venant equations (2D-SVE) of diffusive wave including the difference of bed slope.
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18

Ledoux, Michel. "Analytic and Geometric Logarithmic Sobolev Inequalities." Journées Équations aux dérivées partielles, 2011, 1–15. http://dx.doi.org/10.5802/jedp.79.

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19

Melbourne, James, and Cyril Roberto. "Transport-majorization to analytic and geometric inequalities." Journal of Functional Analysis, September 2022, 109717. http://dx.doi.org/10.1016/j.jfa.2022.109717.

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20

AKYAR, Alaattin. "Some Results on Important Inequalities for Univalent Functions with Positive and Negative Coefficients." Düzce Üniversitesi Bilim ve Teknoloji Dergisi, January 31, 2023, 258–63. http://dx.doi.org/10.29130/dubited.1077414.

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As it is known from Real Analysis, inequalities are used to give the definition of many mathematical concepts formally and to analyze them analytically. Similarly, the geometric characterizations of the range of analytic and univalent functions in the open unit disc U = {z ∈ C : |z| &lt; 1} can be easily analyzed with inequalities and easily classified these functions.
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21

Oladipo, Abiodun Tinuoye. "Analytic Univalent Functions Defined by Generalized Discrete Probability Distribution." Earthline Journal of Mathematical Sciences, August 28, 2020, 169–78. http://dx.doi.org/10.34198/ejms.5121.169178.

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The close-to-convex analogue of a starlike functions by means of generalized discrete probability distribution and Poisson distribution was considered. Some coefficient inequalities and their connection to classical Fekete-Szego theorem are obtained. Our results provide strong connection between Geometric Function Theory and Statistics.
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22

Kassar, Osamah N., and Abdul Rahman S. Juma. "Analytic functions, Subordination, q-Ruscheweyh derivative, Hadamard product, Univalent function." Iraqi Journal of Science, September 29, 2020, 2350–60. http://dx.doi.org/10.24996/ijs.2020.61.9.22.

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In this paper, making use of the q-R uscheweyh differential operator , and the notion of t h e J anowski f unction, we study some subclasses of holomorphic f- unction s . Moreover , we obtain so me geometric characterization like co efficient es timat es , rad ii of starlikeness ,distortion theorem , close- t o- convexity , con vexity, ext reme point s, neighborhoods, and the i nte gral mean inequalities of func tions affiliation to these c lasses
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