منابع مشابه
ON STRONGLY h-CONVEX FUNCTIONS
We introduce the notion of strongly h-convex functions (defined on a normed space) and present some properties and representations of such functions. We obtain a characterization of inner product spaces involving the notion of strongly h-convex functions. Finally, a Hermite–Hadamard–type inequality for strongly h-convex functions is given.
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متن کاملon the quadratic support of strongly convex functions
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.
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In this paper some inequalities for h-convex functions are established. Mathematics Suject Classification: Primary 26D15; Secondary 26A51
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A. Proof of Lemma 1 We need the following lemma that characterizes the property of the extra-gradient descent. Lemma 8 (Lemma 3.1 in (Nemirovski, 2005)). Let Z be a convex compact set in Euclidean space E with inner product 〈·, ·〉, let ‖ · ‖ be a norm on E and ‖ · ‖∗ be its dual norm, and let ω(z) : Z 7→ R be a α-strongly convex function with respect to ‖ · ‖. The Bregman distance associated wi...
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ژورنال
عنوان ژورنال: Annals of Functional Analysis
سال: 2011
ISSN: 2008-8752
DOI: 10.15352/afa/1399900197