On Strongly Convex Functions and Related Classes of Functions

Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 95)

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 

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Copyright information

© Springer Science+Business Media, LLC 2014

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science University of Bielsko-BiałaBielsko-BiałaPoland

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