Results 271 to 280 of about 24,937 (297)

On strongly convex sets and strongly convex functions

Journal of Mathematical Sciences, 2000
The basic notions of this paper are generating set and \(M\)-strongly convex set, which have grown from the axiomatic approach to the notion of convexity. A convex closed set \(M\) of a Banach space \(E\) is called a generating set if for any nonempty set \(A\) of the form \(A=\bigcap_{x\in X}(M+x)\) one can find a convex closed set \(B\subset E\) such
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On the properties of strongly hd convex functions

Annals of the University of Craiova Mathematics and Computer Science Series
We study some optimization properties of $h_d$ strongly convex functions. More precisely, we discuss the characterization properties/inequalities (existence and uniqueness) of minima of $h_d$ strongly convex functions. Moreover, connections with polynomial norms are also presented.
Lăchescu Geanina-Maria, Uță Vasile-Florin   +1 more
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On the Approximation by $\phi$-Strongly Convex Functions

Real Analysis Exchange
The work provides a sandwich type statement for approximating real functions by \(\Phi\)-strongly modulus \(c\) convex functions and some related results, in particular a counterexample showing that similar results do not exist for other types of functions.
Bahos-Orjuela, Cesar M., Herrera-Cruz, Briyith L., Ramos-Fernández, Julio C.   +2 more
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Relative Strongly Exponentially Convex Functions

2020
In this paper, we define and consider some new concepts of the strongly exponentially convex functions involving an arbitrary negative bifunction. Some properties of these strongly exponentially convex functions are investigated under suitable conditions.
Muhammad Aslam Noor, Khalida Inayat Noor, Themistocles M. Rassias   +2 more
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On the quadratic support of strongly convex functions

2015
In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.
Abbaszadeh, S., Eshaghi Gordji, M
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On Strongly Convex Functions and Related Classes of Functions

2014
Many results on strongly convex functions and related classes of functions obtained in the last few years are collected in the paper. In particular, Jensen, Hermite–Hadamard- and Fejer-type inequalities for strongly convex functions are presented. Counterparts of the classical Bernstain–Doetsch and Sierpinski theorems for strongly midconvex functions ...
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A note on strongly convex and quasiconvex functions

Mathematical Notes, 1996
Let \(U\subseteq \mathbb{R}^n\) be a nonempty convex set and let \(J\) be a real-valued function on \(U\). The function \(J\) is said to be: (i) strongly convex on \(U\) if there exists a constant \(r>0\) such that \[ \lambda J(u)+ (1- \lambda)J(v)- J(\lambda u+(1- \lambda)v)\geq r\lambda(1- \lambda)\| u- v\|^2 \] for all \(u,v\in U\), \(\lambda\in[0 ...
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Adequate Criteria for Strongly Starlikeness and Strongly Convexity of Functions

PROOF
T The purpose of this paper is to investigate adequate criteria that ensure the reciprocal of analytic functions to be both strongly starlike and strongly convex within the open unit disk U. Our study leads to the discovery of novel findings.
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Sufficient Conditions for a Minimum of a Strongly Quasiconvex Function on a Weakly Convex Set

Mathematical Notes, 2022
S I Dudov, Dudov S I
exaly  

Strongly log-Convex Functions

Information Sciences Letters, 2021
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