Статті в журналах: "Convolution inequality"

1

Pycia, M. "A convolution inequality." Aequationes Mathematicae 57, no. 2-3 (May 1, 1999): 185–200. http://dx.doi.org/10.1007/s000100050076.

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2

Latała, R., and J. O. Wojtaszczyk. "On the infimum convolution inequality." Studia Mathematica 189, no. 2 (2008): 147–87. http://dx.doi.org/10.4064/sm189-2-5.

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3

Beckner, William. "Pitt's inequality with sharp convolution estimates." Proceedings of the American Mathematical Society 136, no. 05 (November 30, 2007): 1871–86. http://dx.doi.org/10.1090/s0002-9939-07-09216-7.

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4

Walter, W., and V. Weckesser. "An integral inequality of convolution type." Aequationes Mathematicae 46, no. 1-2 (August 1993): 200. http://dx.doi.org/10.1007/bf01834008.

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5

Cwikel, Michael, and Ronald Kerman. "On a convolution inequality of Saitoh." Proceedings of the American Mathematical Society 124, no. 3 (1996): 773–77. http://dx.doi.org/10.1090/s0002-9939-96-03068-7.

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6

Zhao, Junjian, Wei-Shih Du, and Yasong Chen. "New Generalizations and Results in Shift-Invariant Subspaces of Mixed-Norm Lebesgue Spaces ${L_{\vec{p}}(\mathbb{R}^d)}$." Mathematics 9, no. 3 (January 25, 2021): 227. http://dx.doi.org/10.3390/math9030227.

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In this paper, we establish new generalizations and results in shift-invariant subspaces of mixed-norm Lebesgue spaces Lp→(Rd). We obtain a mixed-norm Hölder inequality, a mixed-norm Minkowski inequality, a mixed-norm convolution inequality, a convolution-Hölder type inequality and a stability theorem to mixed-norm case in the setting of shift-invariant subspace of Lp→(Rd). Our new results unify and refine the existing results in the literature.

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7

Oberlin, Daniel M. "A Multilinear Young's Inequality." Canadian Mathematical Bulletin 31, no. 3 (September 1, 1988): 380–84. http://dx.doi.org/10.4153/cmb-1988-054-0.

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8

Borwein, David, та Werner Kratz. "Weighted Convolution Operators on ℓp". Canadian Mathematical Bulletin 48, № 2 (1 червня 2005): 175–79. http://dx.doi.org/10.4153/cmb-2005-015-x.

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9

Christ, Michael, and Qingying Xue. "Smoothness of extremizers of a convolution inequality." Journal de Mathématiques Pures et Appliquées 97, no. 2 (February 2012): 120–41. http://dx.doi.org/10.1016/j.matpur.2011.09.002.

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10

Román-Flores, H., A. Flores-Franulič, and Y. Chalco-Cano. "A convolution type inequality for fuzzy integrals." Applied Mathematics and Computation 195, no. 1 (January 2008): 94–99. http://dx.doi.org/10.1016/j.amc.2007.04.072.

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11

Nielsen, Ole A. "Sharpness in Young's Inequality for Convolution Products." Canadian Journal of Mathematics 46, no. 06 (December 1994): 1287–98. http://dx.doi.org/10.4153/cjm-1994-073-7.

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AbstractSuppose that Gis a locally compact group with modular function Δ and that p, q, r are three numbers in the interval (l,∞) satisfying. If cp,q(G) is the smallest constant c such thatfor all functions f, g ∈ Cc(G) (here the convolution product is with respect to left Haar measure andis the exponent which is conjugate to p) then Young's inequality asserts that cp,q(G) ≤ 1. This paper contains three results about these constants. Firstly, if G contains a compact open subgroup then cp,q(G) = 1 and, as an extension of an earlier result of J. J. F. Fournier, it is shown that there is a constant cp,q< 1 such that if G does not contain a compact open subgroup then c<(G) ≤ c≤. Secondly, Beckner's calculation ofis used to obtain the value of cp,q(G) for all simply-connected solvable Lie groups and all nilpotent Lie groups. And thirdly, it is shown that for a nilpotent Lie group the setis not contained in the union of the spaces Ls(G),.

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12

Feldheim, Naomi, Arnaud Marsiglietti, Piotr Nayar, and Jing Wang. "A note on the convex infimum convolution inequality." Bernoulli 24, no. 1 (February 2018): 257–70. http://dx.doi.org/10.3150/16-bej875.

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13

Cingolani, Silvia, and Tobias Weth. "Trudinger–Moser‐type inequality with logarithmic convolution potentials." Journal of the London Mathematical Society 105, no. 3 (February 15, 2022): 1897–935. http://dx.doi.org/10.1112/jlms.12549.

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14

Cianchi, Andrea, and Bianca Stroffolini. "An Extension of Hedberg's Convolution Inequality and Applications." Journal of Mathematical Analysis and Applications 227, no. 1 (November 1998): 166–86. http://dx.doi.org/10.1006/jmaa.1998.6092.

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15

Lehec, Joseph. "Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems." Canadian Mathematical Bulletin 57, no. 3 (September 1, 2014): 585–97. http://dx.doi.org/10.4153/cmb-2013-040-x.

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AbstractWe give a short proof of the Brascamp–Lieb theorem, which asserts that a certain general formof Young's convolution inequality is saturated by Gaussian functions. The argument is inspired by Borell's stochastic proof of the Prèkopa-Leindler inequality and applies also to the reversed Brascamp-Lieb inequality, due to Barthe.

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16

OLIVEIRA E SILVA, DIOGO, and RENÉ QUILODRÁN. "A comparison principle for convolution measures with applications." Mathematical Proceedings of the Cambridge Philosophical Society 169, no. 2 (June 28, 2019): 307–22. http://dx.doi.org/10.1017/s0305004119000197.

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AbstractWe establish the general form of a geometric comparison principle for n-fold convolutions of certain singular measures in ℝd which holds for arbitrary n and d. This translates into a pointwise inequality between the convolutions of projection measure on the paraboloid and a perturbation thereof, and we use it to establish a new sharp Fourier extension inequality on a general convex perturbation of a parabola. Further applications of the comparison principle to sharp Fourier restriction theory are discussed in the companion paper [3].

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17

Adama, Aïssata, Justin Feuto, and Ibrahim Fofana. "A weighted inequality for potential type operators." Advances in Pure and Applied Mathematics 10, no. 4 (October 1, 2019): 413–26. http://dx.doi.org/10.1515/apam-2018-0101.

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AbstractWe establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on {\mathbb{R}} endowed with a measure which needs not to be doubling.

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18

Essén, Matts, John Rossi, and Daniel Shea. "A convolution inequality with applications to function theory, II." Journal d'Analyse Mathématique 61, no. 1 (December 1993): 339–66. http://dx.doi.org/10.1007/bf02788848.

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19

Duncan, Jennifer. "An Algebraic Brascamp–Lieb Inequality." Journal of Geometric Analysis 31, no. 10 (March 29, 2021): 10136–63. http://dx.doi.org/10.1007/s12220-021-00638-9.

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AbstractThe Brascamp–Lieb inequalities are a very general class of classical multilinear inequalities, well-known examples of which being Hölder’s inequality, Young’s convolution inequality, and the Loomis–Whitney inequality. Conventionally, a Brascamp–Lieb inequality is defined as a multilinear Lebesgue bound on the product of the pullbacks of a collection of functions $$f_j\in L^{q_j}(\mathbb {R}^{n_j})$$ f j ∈ L q j ( R n j ) , for $$j=1,\ldots ,m$$ j = 1 , … , m , under some corresponding linear maps $$B_j$$ B j . This regime is now fairly well understood (Bennett et al. in Geom Funct Anal 17(5):1343–1415, 2008), and moving forward there has been interest in nonlinear generalisations, where $$B_j$$ B j is now taken to belong to some suitable class of nonlinear maps. While there has been great recent progress on the question of local nonlinear Brascamp–Lieb inequalities (Bennett et al. in Duke Math J 169(17):3291–3338, 2020), there has been relatively little regarding global results; this paper represents some progress along this line of enquiry. We prove a global nonlinear Brascamp–Lieb inequality for ‘quasialgebraic’ maps, a class that encompasses polynomial and rational maps, as a consequence of the multilinear Kakeya-type inequalities of Zhang and Zorin-Kranich. We incorporate a natural affine-invariant weight that both compensates for local degeneracies and yields a constant with minimal dependence on the underlying maps. We then show that this inequality generalises Young’s convolution inequality on algebraic groups with suboptimal constant.

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20

Priya, Kuppuraj Divya, and K. Thilagavathi. "Geometric Properties of Harmonic Function Affiliated With Fractional Operator." International Journal of Analysis and Applications 22 (August 12, 2024): 133. http://dx.doi.org/10.28924/2291-8639-22-2024-133.

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This paper's goal is to discover new results for the harmonic univalent functions G=υ+η defined in the open unit disc ρ={z: |z|<1}. Examining KS indicates the set of all analytic harmonic functions of form G in the open unit disc ρ. The convolution featuring the Mittag-Leffler function and fractional operator is applied to generate the family of harmonic univalent VKS. Motivated by Kamali [9], we present a novel of kamali class with VKS(δ) brand-new class of harmonic univalent functions Pα,β,zγ,δ,ε,ν inspiring inequality. Analysing Mittag-Leffler function convolution with modified tremblay operator inequality as a necessary and sufficient condition for univalent harmonic functions related to specific generalised Mittag-Leffler functions to be in the function class VKS(δ) is the aim of this research. Moreover, we discover extreme points, a distortion theorem, convolution properties, and convex combinations for the functions in VKS(δ).

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21

DA PELO, PAOLO, ALBERTO LANCONELLI, and AUREL I. STAN. "A HÖLDER–YOUNG–LIEB INEQUALITY FOR NORMS OF GAUSSIAN WICK PRODUCTS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 14, no. 03 (September 2011): 375–407. http://dx.doi.org/10.1142/s0219025711004456.

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An important connection between the finite-dimensional Gaussian Wick products and Lebesgue convolution products will be proven first. Then this connection will be used to prove an important Hölder inequality for the norms of Gaussian Wick products, reprove Nelson hypercontractivity inequality, and prove a more general inequality whose marginal cases are the Hölder and Nelson inequalities mentioned before. We will show that there is a deep connection between the Gaussian Hölder inequality and classic Hölder inequality, between the Nelson hypercontractivity and classic Young inequality with the sharp constant, and between the third more general inequality and an extension by Lieb of the Young inequality with the best constant. Since the Gaussian probability measure exists even in the infinite-dimensional case, the above three inequalities can be extended, via a classic Fatou's lemma argument, to the infinite-dimensional framework.

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22

Wang, Zhi-Gang, and Ming-Liang Li. "Some properties of certain family of multiplier transforms." Filomat 31, no. 1 (2017): 159–73. http://dx.doi.org/10.2298/fil1701159w.

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The main purpose of this paper is to derive some inequality properties, convolution properties, subordination and superordination properties, and sandwich-type results of a certain family of multiplier transforms.

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23

Muzychuk, A. O. "The Laguerre transform of a convolution product of vector-valued functions." Matematychni Studii 55, no. 2 (June 23, 2021): 146–61. http://dx.doi.org/10.30970/ms.55.2.146-161.

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The Laguerre transform is applied to the convolution product of functions of a real argument (over the time axis) with values in Hilbert spaces. The main results have been obtained by establishing a relationship between the Laguerre and Laplace transforms over the time variable with respect to the elements of Lebesgue weight spaces. This relationship is built using a special generating function. The obtained dependence makes it possible to extend the known properties of the Laplace transform to the case of the Laguerre transform. In particular, this approach concerns the transform of a convolution of functions. The Laguerre transform is determined by a system of Laguerre functions, which forms an orthonormal basis in the weighted Lebesgue space. The inverse Laguerre transform is constructed as a Laguerre series. It is proven that the direct and the inverse Laguerre transforms are mutually inverse operators that implement an isomorphism of square-integrable functions and infinite squares-summable sequences. The concept of a q-convolution in spaces of sequences is introduced as a discrete analogue of the convolution products of functions. Sufficient conditions for the existence of convolutions in the weighted Lebesgue spaces and in the corresponding spaces of sequences are investigated. For this purpose, analogues of Young’s inequality for such spaces are proven. The obtained results can be used to construct solutions of evolutionary problems and time-dependent boundary integral equations.

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24

Dmytryshyn, M. I. "Approximation by interpolation spectral subspaces of operators with discrete spectrum." Matematychni Studii 55, no. 2 (June 22, 2021): 162–70. http://dx.doi.org/10.30970/ms.55.2.162-170.

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Анотація:

The Laguerre transform is applied to the convolution product of functions of a real argument (over the time axis) with values in Hilbert spaces. The main results have been obtained by establishing a relationship between the Laguerre and Laplace transforms over the time variable with respect to the elements of Lebesgue weight spaces. This relationship is built using a special generating function. The obtained dependence makes it possible to extend the known properties of the Laplace transform to the case of the Laguerre transform. In particular, this approach concerns the transform of a convolution of functions. The Laguerre transform is determined by a system of Laguerre functions, which forms an orthonormal basis in the weighted Lebesgue space. The inverse Laguerre transform is constructed as a Laguerre series. It is proven that the direct and the inverse Laguerre transforms are mutually inverse operators that implement an isomorphism of square-integrable functions and infinite squares-summable sequences. The concept of a q-convolution in spaces of sequences is introduced as a discrete analogue of the convolution products of functions. Sufficient conditions for the existence of convolutions in the weighted Lebesgue spaces and in the corresponding spaces of sequences are investigated. For this purpose, analogues of Young’s inequality for such spaces are proven. The obtained results can be used to construct solutions of evolutionary problems and time-dependent boundary integral equations.

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25

Ndungi, Rebeccah, and Samuel Karuga. "Sign Language Prediction Model using Convolution Neural Network." IJID (International Journal on Informatics for Development) 10, no. 2 (February 5, 2022): 92–101. http://dx.doi.org/10.14421/ijid.2021.3284.

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The barrier between the hearing and the deaf communities in Kenya is a major challenge leading to a major gap in the communication sector where the deaf community is left out leading to inequality. The study used primary and secondary data sources to obtain information about this problem, which included online books, articles, conference materials, research reports, and journals on sign language and hand gesture recognition systems. To tackle the problem, CNN was used. Naturally captured hand gesture images were converted into grayscale and used to train a classification model that is able to identify the English alphabets from A-Z. Then identified letters are used to construct sentences. This will be the first step into breaking the communication barrier and the inequality. A sign language recognition model will assist in bridging the exchange of information between the deaf and hearing people in Kenya. The model was trained and tested on various matrices where we achieved an accuracy score of a 99% value when run on epoch of 10, the log loss metric returning a value of 0 meaning that it predicts the actual hand gesture images. The AUC and ROC curves achieved a 0.99 value which is excellent.

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26

Strzelecka, Marta, Michal Strzelecki, and Tomasz Tkocz. "On the convex infimum convolution inequality with optimal cost function." Latin American Journal of Probability and Mathematical Statistics 14, no. 1 (2017): 903. http://dx.doi.org/10.30757/alea.v14-39.

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27

Itoh, Yoshiaki. "An application of the convolution inequality for the Fisher information." Annals of the Institute of Statistical Mathematics 41, no. 1 (March 1989): 9–12. http://dx.doi.org/10.1007/bf00049105.

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28

Bui, Huy-Qui. "Weighted Young's Inequality and Convolution Theorems on Weighted Besov Spaces." Mathematische Nachrichten 170, no. 1 (November 11, 2006): 25–37. http://dx.doi.org/10.1002/mana.19941700104.

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29

Atshan, Waggas Galib, and Fatimah Hayder Hasan. "On a New Subclass of Univalent Harmonic Functions That Defined by Integral Operator." Journal of Kufa for Mathematics and Computer 4, no. 2 (June 30, 2017): 40–46. http://dx.doi.org/10.31642/jokmc/2018/040206.

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In this paper, we investigate several properties of the harmonic class ( ) we discuss the coefficient inequality, the distortion bounds theorem, the closure theorem, convex combinations, Bernardi integral operator and integral convolution property.

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30

Kerman, R. A. "Convolution with Odd Kernels Having a Tempered Singularity." Canadian Mathematical Bulletin 31, no. 1 (March 1, 1988): 3–12. http://dx.doi.org/10.4153/cmb-1988-001-6.

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AbstractSuppose b(t) decreases to 0 on [1, ∞). Define the singular integral operator Cb at periodic f of period 1 in L1 (T),T = ( - 1 / 2, 1/2), byThen, for a large class of b one has the rearrangement inequalityThis inequality is used to construct a rearrangement invariant function space X corresponding to a given such space Y so that Cb maps X into Y.

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31

Raza, Mohsan, Muhammad Arif, and Maslina Darus. "Fekete-Szegő Inequality for a Subclass ofp-Valent Analytic Functions." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/127615.

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The main object of this paper is to study Fekete-Szegő problem for the class ofp-valent functions. Fekete-Szegő inequality of several classes is obtained as special cases from our results. Applications of the results are also obtained on the class defined by convolution.

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32

GUPTA, Vimlesh, Saurabh PORWAL, and Omendra MİSHRA. "Multivalent harmonic functions Involving multiplier transformation." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 3 (September 30, 2022): 731–51. http://dx.doi.org/10.31801/cfsuasmas.962040.

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In the present investigation we study a subclass of multivalent harmonic functions involving multiplier transformation. An equivalent convolution class condition and a sufficient coefficient condition for this class is acquired. We also show that this coefficient condition is necessary for functions belonging to its subclass. As an application of coefficient condition, a necessary and sufficient hypergeometric inequality is also given. Further, results on bounds, inclusion relation, extreme points, a convolution property and a result based on the integral operator are obtained.

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33

Křepela, Martin. "Convolution in Weighted Lorentz Spaces of Type $\Gamma$." MATHEMATICA SCANDINAVICA 119, no. 1 (August 19, 2016): 113. http://dx.doi.org/10.7146/math.scand.a-24187.

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We characterize boundedness of the convolution operator between weighted Lorentz spaces $\Gamma^p(v)$ and $\Gamma^q(w)$ for the range of parameters $p,q\in[1,\infty]$, or $p\in(0,1)$ and $q\in\{1,\infty\}$, or $p=\infty$ and $q\in(0,1)$. We provide Young-type convolution inequalities of the form \[ \|f\ast g\|_{\Gamma^q(w)} \le C \|f\|_{\Gamma^p(v)}\|g\|_Y, \quad f\in\Gamma^p(v), g\in Y, \] characterizing the optimal rearrangement-invariant space $Y$ for which the inequality is satisfied.

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34

Seoudy, T. M., and M. K. Aouf. "ON CERTAIN SUBCLASS OF p-VALENT NON-BAZILEVIC FUNCTIONS DEFINED BY THE DZIOK–SRIVASTAVA OPERATOR." Asian-European Journal of Mathematics 06, no. 03 (September 2013): 1350032. http://dx.doi.org/10.1142/s1793557113500320.

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By making use of the principle of subordination and Dziok–Srivastava operator, we introduce a certain subclass of p-valent non-Bazilevic analytic functions. Such results as subordination and superordination properties, convolution properties, distortion theorems and inequality properties, are proved.

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35

Bessenyei, Mihály, and Zsolt Páles. "Characterization of higher-order monotonicity via integral inequalities." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, no. 4 (August 2010): 723–36. http://dx.doi.org/10.1017/s0308210509001188.

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The Hermite-Hadamard inequality not only is a consequence of convexity but also characterizes it: if a continuous function satisfies either its left-hand side or its right-hand side on each compact subinterval of the domain, then it is necessarily convex. The aim of this paper is to prove analogous statements for the higher-order extensions of the Hermite-Hadamard inequality. The main tools of the proofs are smoothing by convolution and the support properties of higher-order monotone functions.

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36

Selvaraj, C., K. R. Karthikeyan, and S. Lakshmi. "Fekete-Szegö Inequalities of a Subclass of Multivalent Analytic Functions." Annals of West University of Timisoara - Mathematics and Computer Science 54, no. 1 (July 1, 2016): 167–83. http://dx.doi.org/10.1515/awutm-2016-0010.

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Анотація:

Abstract The main object of this paper is to study Fekete-Szegö problem for a certain subclass of p - valent analytic functions. Fekete-Szegö inequality of several classes are obtained as special cases from our results. Applications of the result are also obtained on the class defined by convolution.

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37

Soni, Amit, and Shashi Kant. "A New Subclass of Meromorphic Close-to-Convex Functions." Journal of Complex Analysis 2013 (January 8, 2013): 1–5. http://dx.doi.org/10.1155/2013/629394.

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Анотація:

A new subclass MK(t, A, B) of meromorphic close-to-convex functions, defined by means of subordination, is investigated. Some results such as inclusion relationship, coefficient inequality, convolution property, and distortion property for this class are derived. The results obtained here are extension of earlier known work.

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38

Borys, Andrzej. "On Bounds on Cumulative Teletraffic Using Min-Plus Convolution." International Journal of Electronics and Telecommunications 58, no. 4 (December 1, 2012): 315–22. http://dx.doi.org/10.2478/v10177-012-0043-1.

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Abstract Ideas and results published in two papers by R. L. Cruz in IEEE Transactions on Information Theory in 1991 gave rise to what is called now network calculus. A key role in it plays a certain inequality characterizing the behaviour of cumulative traffic curves. It defines the so-called burstiness constraint by which many kinds of traffics can be described, as for example those occurring in computer networks. Interpretation of this constraint, which can be expressed in two equivalent forms: with and without the use of min-plus convolution, can be found in papers of R. L. Cruz. Nothing however was said about how to obtain it practically, for example, for each of representatives of a family of measured cumulative traffic curves being upperbounded. This problem is tackled in this paper, and as a result, a relation between the Cruz’s constraining function and an upper-bounding function of measured traffic curves is found. The relation obtained is quite general and valid also for the case of non-fulfilment of the so-called sub-additivity property by traffic curves. For the purpose of its derivation, a notion of sub-additivity property with some tolerance Δ was introduced, and the corresponding theorem exploiting it formulated and proved. Further, to complement discussion of the above relation, a minimal burstiness constraint was added to the original Cruz’s inequality and related with a lower bound of a family of measured cumulative traffic curves. The derivations presented in this paper are illustrated by examples.

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39

Atshan, Waggas Galib, and Abdul Jalil G. Khalaf. "On a New Class of Meromorphic Univalent Function Associated with Dziok_Srivastava Operator." Journal of Kufa for Mathematics and Computer 2, no. 2 (December 1, 2014): 56–63. http://dx.doi.org/10.31642/jokmc/2018/020209.

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Анотація:

In this paper, we introduce and study a new class of meromorphic Univalent functions deï¬ned by Dziok_Srivastava operator for this class. We obtain coefficient inequality, convex set, closure and Hadamard product (or convolution).Further we obtain a(n,Î´)-neighborhood of the function fâˆˆ Ï‘, and the integral transform.

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40

Mahdi, Mohammed Maad, Waggas Galib Atshan, and Abdul Jalil M. Khalaf. "On a New Class of Meromorphic Univalent Function Associated with Dziok_Srivastava Operator." Journal of Kufa for Mathematics and Computer 2, no. 3 (June 30, 2015): 56–63. http://dx.doi.org/10.31642/jokmc/2018/020305.

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Анотація:

In this paper, we introduce and study a new class of meromorphic Univalent functions deï¬ned by Dziok_Srivastava operator for this class. We obtain coefficient inequality, convex set, closure and Hadamard product (or convolution).Further we obtain a(n,Î´)-neighborhood of the function fâˆˆ Ï‘, and the integral transform.

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41

A. Al-Saphory, Raheam, Abdul Rahman S. Juma, and Ali H. Maran. "Certain Subclass of Harmonic Multivalent Functions Defined by New Linear Operator." Wasit Journal for Pure sciences 3, no. 3 (September 30, 2024): 1–8. http://dx.doi.org/10.31185/wjps.422.

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Анотація:

The main goal of the present paper is to introduce a new class of harmonic multivalent functions defined by a new linear operator in the open unit disc . Thus, some geometric properties have examined, including coefficient inequality, extreme points, convolution conditions, convex linear combinations, and integral transforms for the class .

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42

Khan, Mohammad Faisal, Khaled Matarneh, Shahid Khan, Saqib Hussain, and Maslina Darus. "New Class of Close-to-Convex Harmonic Functions Defined by a Fourth-Order Differential Inequality." Journal of Mathematics 2022 (August 13, 2022): 1–9. http://dx.doi.org/10.1155/2022/4051867.

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Анотація:

In the recent past, various new subclasses of normalized harmonic functions have been defined in open unit disk U which satisfy second-order and third-order differential inequalities. Here, in this study, we define a new class of normalized harmonic functions in open unit disk U which is satisfying a fourth-order differential inequality. We investigate some useful results such as close-to-convexity, coefficient bounds, growth estimates, sufficient coefficient condition, and convolution for the functions belonging to this new class of harmonic functions. In addition, under convex combination and convolution of its members, we prove that this new class is closed, and we also give some lemmas to prove our main results.

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43

Katkovskaya, I. N., and V. G. Krotov. "Strong-Type Inequality for Convolution with Square Root of the Poisson Kernel." Mathematical Notes 75, no. 3/4 (March 2004): 542–52. http://dx.doi.org/10.1023/b:matn.0000023335.53027.30.

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44

Vijaya, K., G. Murugusundaramoorthy, and M. Kasthuri. "Pascu-Type Harmonic Functions with Positive Coefficients Involving Salagean Operator." International Journal of Analysis 2014 (April 6, 2014): 1–10. http://dx.doi.org/10.1155/2014/793709.

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Анотація:

Making use of a Salagean operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc. Among the results presented in this paper including the coeffcient bounds, distortion inequality, and covering property, extreme points, certain inclusion results, convolution properties, and partial sums for this generalized class of functions are discussed.

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45

Wu, Xiaolei, and Yubin Yan. "Error Analysis for Semilinear Stochastic Subdiffusion with Integrated Fractional Gaussian Noise." Mathematics 12, no. 22 (November 15, 2024): 3579. http://dx.doi.org/10.3390/math12223579.

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Анотація:

We analyze the error estimates of a fully discrete scheme for solving a semilinear stochastic subdiffusion problem driven by integrated fractional Gaussian noise with a Hurst parameter H∈(0,1). The covariance operator Q of the stochastic fractional Wiener process satisfies ∥A−ρQ1/2∥HS < ∞ for some ρ∈[0,1), where ∥·∥HS denotes the Hilbert–Schmidt norm. The Caputo fractional derivative and Riemann–Liouville fractional integral are approximated using Lubich’s convolution quadrature formulas, while the noise is discretized via the Euler method. For the spatial derivative, we use the spectral Galerkin method. The approximate solution of the fully discrete scheme is represented as a convolution between a piecewise constant function and the inverse Laplace transform of a resolvent-related function. By using this convolution-based representation and applying the Burkholder–Davis–Gundy inequality for fractional Gaussian noise, we derive the optimal convergence rates for the proposed fully discrete scheme. Numerical experiments confirm that the computed results are consistent with the theoretical findings.

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46

Elrifai, E. A., H. E. Darwish, and A. R. Ahmed. "Some Properties of Certain Multivalent Analytic Functions Involving the Cătas Operator." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–25. http://dx.doi.org/10.1155/2011/752341.

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Анотація:

We introduce a certain subclass of multivalent analytic functions by making use of the principle of subordination between these functions and Cătas operator. Such results as subordination and superordination properties, convolution properties, inclusion relationships, distortion theorems, inequality properties, and sufficient conditions for multivalent starlikeness are provide. The results presented here would provide extensions of those given in earlier works. Several other new results are also obtained.

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47

AL-KHAFAJI, AQEEL KETAB, and ABBAS KAREEM WANAS. "Certain Properties on Meromorphic Functions Defined by a New Linear Operator Involving the Mittag-Leffler Function." Kragujevac Journal of Mathematics 48, no. 3 (2024): 473–83. http://dx.doi.org/10.46793/kgjmat2403.473ak.

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Анотація:

Our paper introduces a new linear operator using the convolution between a Mittag–Leffler Function and basic hypergeometric function. Use of the linear operator creates a new class of meromorphic functions defined in the punctured open unit disk. Consequently, the paper examines different aspects Apps and assets like, extreme points, coefficient inequality, growth and distortion. In conclusion, the work discusses modified Hadamard product and closure theorems.

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48

Lashin, Abdel Moneim Y., Abeer O. Badghaish, and Fayzah A. Alshehri. "Properties for a Certain Subclass of Analytic Functions Associated with the Salagean q-Differential Operator." Fractal and Fractional 7, no. 11 (October 30, 2023): 793. http://dx.doi.org/10.3390/fractalfract7110793.

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Анотація:

Using the Salagean q-differential operator, we investigate a novel subclass of analytic functions in the open unit disc, and we use the Hadamard product to provide some inclusion relations. Furthermore, the coefficient conditions, convolution properties, and applications of the q-fractional calculus operators are investigated for this class of functions. In addition, we extend the Miller and Mocanu inequality to the q-theory of analytic functions.

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49

Sadowski, Jacek. "Young's inequality for convolution and its applications in convex- and set-valued analysis." Journal of Mathematical Analysis and Applications 421, no. 2 (January 2015): 1274–94. http://dx.doi.org/10.1016/j.jmaa.2014.07.045.

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50

Lin, Yufeng, and Jiawen He. "Existence of Solutions for a Class of Nonlinear Convolution Integral Equations." Highlights in Science, Engineering and Technology 70 (November 15, 2023): 351–59. http://dx.doi.org/10.54097/hset.v70i.13882.

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Анотація:

The existence, uniqueness, boundedness and monotonicity of solutions for a class of nonlinear convolutional integral equations are discussed. First, the problem of solving the equation is transformed into a fixed-point problem of an operator. Then, Arzela – Ascoli theorem and Schauder fixed point theorem are used to prove the existence of the solution. Then, Gronwall inequality and its related lemma are used to prove the uniqueness of the solution. Secondly, the sufficient and necessary conditions for boundedness of nonnegative solutions are given by using the supremum principle and Weierstrass aggregation point theorem. Finally, under given conditions, the monotonicity of the nonnegative solution is discussed, which extends the existing results.

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