We introduce new versions of uniformly convex functions, namely h(d) strongly (weaker) convexfunctions. Based on the positivity of complete homogeneous symmetric polynomials with even degree, recently studied in Rove...
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We introduce new versions of uniformly convex functions, namely h(d) strongly (weaker) convexfunctions. 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 uniformlyconvexity. 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.
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 ...
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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.
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} \us...
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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.
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 inequaliti...
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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.
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 ...
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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 uniformlyconvex 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.
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 ...
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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 convexfunctions as well as for the class of starlike functions with respect to a boundary point. (c) 2020 Elsevier Inc. All rights reserved.
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...
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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 distortion bounds, radii of starlikeness and convexity and modified Hadamard products.
In this paper, we introduce notable Jensen-Mercer inequality for a general class of convexfunctions, namely uniformly convex functions. We explore some interesting properties of such a class of functions along with s...
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In this paper, we introduce notable Jensen-Mercer inequality for a general class of convexfunctions, 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).
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 conv...
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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.
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) + ...
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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 convexfunctions, 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.
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