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On Strongly Convex Functions and Related Classes of Functions

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Handbook of Functional Equations

Part of the book series: Springer Optimization and Its Applications ((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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science University of Bielsko-Biała, ul.Willowa 2, 43–309, Bielsko-Biała, Poland

    Kazimierz Nikodem

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  1. Kazimierz Nikodem
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Correspondence to Kazimierz Nikodem .

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  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Nikodem, K. (2014). On Strongly Convex Functions and Related Classes of Functions. In: Rassias, T. (eds) Handbook of Functional Equations. Springer Optimization and Its Applications, vol 95. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1246-9_16

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