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New Versions of uniformly convex functions via Quadratic Complete Homogeneous Symmetric Polynomials

MEDITERRANEAN JOURNAL OF MATHEMATICS 2023年第5期20卷 279-279页

作者： Lachescu, Geanina Maria Malin, Maria Roventa, Ionel Univ Craiova Dept Math AI Cuza St 13 Craiova 200585 Romania

We introduce new versions of uniformly convex functions, namely h(d) strongly (weaker) convex functions. Based on the positivity of complete homogeneous symmetric polynomials with even degree, recently studied in Roventa and Temereanc (Mediterr J Math 16:1- 16, 2019), Rovent,a et al. (A note on weighted Ingham's inequality for families of exponentials with no gap, In: 24th ICSTCC, pp 43-48, 2020;Weighted Ingham's type inequalities via the positivity of quadratic polynomials, submitted), and Tao (https://***/2017/ 08/06/schur-convexity-and-positive-definiteness-of-the-even-degree-complete-homogeneous-symmetric-polynomials/), we introduce stronger and weaker versions of uniformly convexity. In this context, we recover well-known type inequalities such as: Jensen's, Hardy-Littlewood- Polya's and Popoviciu's inequalities. Some final remarks related to Sherman's and Ingham's type inequalities are also discussed.

关键词： & nbsp Complete homogeneous symmetric polynomials uniformly convex functions h(d) strongly convex function Schur-convex functions majorization theory

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New classes of uniformly convex functions of fractional power on Banach space

ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS

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ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS 2020年第43期43卷 926-933页

作者： Abdulnaby, Zainab E. Mustansiriyah Univ Coll Sci Dept Math Baghdad Iraq

The aim of this paper is to define new certain subclasses of analytic functions of fractional parameters in the well-known unit disk U. Then introduce and study a new integral operator type fractional in the sense of Noor integral on Banach space. In addition, some of its applications are discussed by utilizing a Owa-Hadamard product.

关键词： analytic functions Owa-Hadamard product uniformly convex functions Banach space

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Ma-Minda Starlikeness of Univalent functions

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RESULTS IN MATHEMATICS 2025年第2期80卷 1-11页

作者： Lecko, Adam Madhumitha, Saravanarasu Ravichandran, Vaithiyanathan Univ Warmia & Mazury Fac Math & Comp Sci Dept Complex Anal Ul Sloneczna 54 PL-10710 Olsztyn Poland Kongu Engn Coll Dept Math Perundurai 638060 Tamilnadu India Natl Inst Technol Dept Math Trichy 620015 Tamilnadu India

A normalized analytic function f defined on the unit disk is Ma-Minda starlike (with respect to phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}) if the quantity zf '(z)/f(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$zf'(z)/f(z)$$\end{document} is subordinate to the function phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}. The radius of starlikeness and parabolic starlikeness of the class S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {S}$$\end{document} of univalent functions on the unit disk are well-known. In this paper, we determine the radii of functions in S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {S}$$\end{document} to belong to several well-known classes of Ma-Minda starlike functions.

关键词： Starlike functions subordination radius problem uniformly convex functions Ma-Minda starlike functions

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On Some Inequalities of Differentiable uniformly convex Mapping with Applications

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2023年第5期44卷 368-381页

作者： Barsam, Hasan Sayyari, Yamin Univ Jiroft Dept Math Jiroft Iran Sirjan Univ Technol Dept Math Sirjan Iran

The widely known hermite-hadamard-Fejer type inequalities are so important in the field of mathematical analysis. Many researchers have studied on these inequalities. In this paper, we have obtained several inequalities related to the Hermite-Hadamard inequality for a special class of the functions called uniformly convex functions. We have also presented applications of these obtained inequalities in some error estimates for higher moments of random variables.

关键词： Hermite-Hadamard inequality integral inequalities random variable uniformly convex functions

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Mirror Descent Strikes Again: Optimal Stochastic convex Optimization under Infinite Noise Variance 35

Mirror Descent Strikes Again: Optimal Stochastic Convex Opti...

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35th Conference on Learning Theory (COLT)

作者： Vural, Nuri Mert Yu, Lu Balasubramanian, Krishnakumar Volgushev, Stanislav Erdogdu, Murat A. Univ Toronto Dept Comp Sci Toronto ON Canada Vector Inst Toronto ON Canada Univ Toronto Dept Stat Sci Toronto ON Canada Univ Calif Davis Dept Stat Davis CA 95616 USA

We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded (1+ k)-th moment, for some k is an element of (0;1], we quantify the convergence rate of the Stochastic Mirror Descent algorithm with a particular class of uniformly convex mirror maps, in terms of the number of iterations, dimensionality and related geometric parameters of the optimization problem. Interestingly this algorithm does not require any explicit gradient clipping or normalization, which have been extensively used in several recent empirical and theoretical works. We complement our convergence results with information-theoretic lower bounds showing that no other algorithm using only stochastic first-order oracles can achieve improved rates. Our results have several interesting consequences for devising online/streaming stochastic approximation algorithms for problems arising in robust statistics and machine learning.

关键词： Mirror descent algorithm uniformly convex functions heavy-tailed gradient noise oracle complexity information-theoretic lower bounds

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Bohr radius for certain classes of starlike and convex univalent functions

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2021年第1期493卷 124519-124519页

作者： Allu, Vasudevarao Halder, Himadri Indian Inst Technol Bhubaneswar Sch Basic Sci Bhubaneswar 752050 Odisha India

We say that a class F consisting of analytic functions f (z) = E-n=0 infinity a(n)z(n) in the unit disk D := {z E C : vertical bar z vertical bar < 1} satisfies a Bohr phenomenon if there exists r(f) is an element of (0, 1) such that Sigma(infinity)(n=1) vertical bar a(n)z(n)vertical bar <= d(f (0) partial derivative f (D)) for every function f is an element of F and 1 vertical bar z vertical bar = r <= r(f), where d is the Euclidean distance. The largest radius r(f) is the Bohr radius for the class F. In this paper, we establish the Bohr phenomenon for the classes consisting of Ma-Minda type starlike functions and Ma-Minda type convex functions as well as for the class of starlike functions with respect to a boundary point. (c) 2020 Elsevier Inc. All rights reserved.

关键词： Univalent Starlike convex uniformly starlike uniformly convex functions Bohr radius

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Certain subclasses of uniformly convex functions of order α and type β with varying arguments

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Journal of the Egyptian Mathematical Society 2013年第3期21卷 184-189页

作者： N. Magesh P.G. and Research Department of Mathematics Govt. Arts College for Men Krishnagiri 635 001 India

In this paper, we define a new subclass of k -uniformly convex functions order α type β with varying argument of coefficients and obtain coefficient estimates. Further we investigate extreme points, growth and disto... 详细信息

关键词： 30C45 Univalent functions convex functions Starlike functions uniformly convex functions uniformly starlike functions

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On some inequalities for uniformly convex mapping with estimations to normal distributions

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2023年第1期2023卷 89-89页

作者： Butt, Saad Ihsan Sayyari, Yamin Agarwal, Praveen Nieto, Juan J. Umar, Muhammad COMSATS Univ Islamabad Dept Math Lahore Campus Lahore Pakistan Sirjan Univ Technol Dept Math Sirjan Iran Anand Int Coll Engn Dept Math Jaipur India Ajman Univ Nonlinear Dynam Res Ctr NDRC Ajman U Arab Emirates Univ Santiago Compostela Dept Stat CITMAga Santiago De Compostela 15882 Spain

In this paper, we introduce notable Jensen-Mercer inequality for a general class of convex functions, namely uniformly convex functions. We explore some interesting properties of such a class of functions along with some examples. As a result, we establish Hermite-Jensen-Mercer inequalities pertaining uniformly convex functions by considering the class of fractional integral operators. Moreover, we establish Mercer-Ostrowski inequalities for conformable integral operator via differentiable uniformly convex functions. Finally, we apply our inequalities to get estimations for normal probability distributions (Gaussian distributions).

关键词： Hermite-Mercer inequality uniformly convex functions Integral inequalities Fractional integrals

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Averaging operators and the classes of starlike functions related to parabola

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ANALYSIS AND MATHEMATICAL PHYSICS 2020年第1期10卷 1-7页

作者： Sokol, Janusz Wisniowska-Wajnryb, Agnieszka Univ Rzeszow Coll Nat Sci Prof Pigonia St 1 PL-35310 Rzeszow Poland Rzeszow Univ Technol Fac Math & Appl Phys Powstancow Warszawy Ave 12 PL-35959 Rzeszow Poland

An operator I is said to be an averaging (or mean-value) operator on a set kappa of analytic functions in Delta = {z : vertical bar z vertical bar < 1}, if I [f](0) = f (0) and I [f](Delta) is contained in the convex hull of f (Delta) for all f epsilon kappa. In this work we consider the class SP(alpha) of functions defined by us (Folia Sci Univ Technol Resov 28:35-42, 1993), which is connected with the class of uniformly convex functions introduced by Goodman (Ann Polon Math 56:87-92, 1991). We describe an interesting new construction of averaging operators which might attract a considerable attention of mathematicians working in the field.

关键词： Averaging integral operator uniformly convex functions Starlike functions convex functions

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An application of Mittag-Leffler-type Poisson distribution on certain subclasses of analytic functions associated with conic domains

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HELIYON 2021年第10期7卷 e08109页

作者： Ahmad, Morad Frasin, Basem Murugusundaramoorthy, Gangadharan Al-Khazaleh, Ahmad Univ Jordan Dept Math Amman 11942 Jordan Al al Bayt Univ Fac Sci Dept Math Mafraq Jordan Deemed Univ Vellore Sch Adv Sci Vellore Inst Technol Vellore 632014 Tamil Nadu India

In this paper our aim is to deduce some sufficient conditions and inclusion properties for Mittag-Leffler-type Poisson distribution series Psi(m)(a,beta)(z)=z+Sigma(infinity Gamma(beta))(n=2)m(n-1/Gamma(alpha()n-1) + beta)(Ea+beta(m)(z)n to be in the classes k-ST[A,B] and k-UCV[A,B] of k-uniformly Janowski starlike and k-Janowski convex functions, respectively. Further, we obtain a condition for an integral operator G(a,beta)(m)(z)=integral(z)(0)a(m)/beta(t)tdt to be in the class k-UCV[A,B]. Several corollaries and consequences of the main results are also considered.

关键词： Starlike functions convex functions uniformly starlike functions uniformly convex functions Hadamard product Mittag-Leffler function

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