Results 211 to 220 of about 13,789 (256)

Quartic Regularity. [PDF]

open access: yesVietnam J Math
Nesterov Y.
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Converse Ohlin’s lemma for convex and strongly convex functions

Journal of Applied Analysis, 2022
Abstract Theorems which are converse to the Ohlin lemma for convex and strongly convex functions are proved. New proofs of probabilistic characterizations of convex and strongly convex functions are presented.
Mirosław Adamek, Kazimierz Nikodem
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Strongly E-convex sets and strongly E-convex functions

Journal of Interdisciplinary Mathematics, 2005
Abstract A class of E-convex sets and a class of E-convex functions are extended to the so called strongly E-convex sets and strongly E-convex functions. In this extension we take into account the images of two points x and y under an E : Rn → Rn operator besides the two points themselves.
E. A. Youness, Tarek Emam
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Remarks on strongly convex functions

Aequationes mathematicae, 2010
Let \(I\subseteq \mathbb{R}\) be an interval and \(c\) be a positive number. A function \(f:I\rightarrow \mathbb{R}\) is called strongly convex with modulus \( c\) if \[ f(tx+(1-t)y)\leq tf(x)+(1-t)f(y)-ct(1-t)(x-y)^{2}, \] for all \(x,y\in I\) and \(t\in [0,1]\).
Merentes, Nelson, Nikodem, Kazimierz
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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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