On Strongly Convex Functions and Related Classes of Functions

Kazimierz Nikodem ()
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Kazimierz Nikodem: Department of Mathematics and Computer Science University of Bielsko-Biała

A chapter in Handbook of Functional Equations, 2014, pp 365-405 from Springer

Abstract: Abstract 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 Fejér-type inequalities for strongly convex functions are presented. Counterparts of the classical Bernstain–Doetsch and Sierpiński theorems for strongly midconvex functions are given. New characterizations of inner product spaces involving strong convexity are obtained. A representation of strongly Wright-convex functions and a characterization of functions generating strongly Schur-convex sums are presented. Strongly n-convex and Jensen n-convex functions are investigated. Finally, a relationship between strong convexity and generalized convexity in the sense of Beckenbach is established.

Keywords: Strongly convex (midconvex; Wright-convex; Schur-convex; h-convex; n-convex) function; Jensen (Hermite–Hadamard; Fejér) inequality; Inner product space; Generalized convex function (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1246-9_16

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DOI: 10.1007/978-1-4939-1246-9_16

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