Applications of quasiconvexity

S. Abramovich

doi:10.1007/978-3-319-31317-7_1

Applications of quasiconvexity

S. Abramovich

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

This survey deals with functions called γ-quasiconvex functions and their relations to convexity and superquadracity. For γ-quasiconvex functions and for superquadratic functions, we get analogs of inequalities satisfied by convex functions and we get refinements for those convex functions which are also γ-quasiconvex as well as superquadratic. We show in which cases the refinements by γ-quasiconvex functions are better than those obtained by superquadratic functions and convex functions. The power functions defined on x ≥ 0 where the power is greater or equal to two are examples of convex, quasiconvex, and superquadratic functions.

Original language	English
Title of host publication	Contributions in Mathematics and Engineering
Subtitle of host publication	In Honor of Constantin Caratheodory
Publisher	Springer International Publishing
Pages	1-23
Number of pages	23
ISBN (Electronic)	9783319313177
ISBN (Print)	9783319313153
DOIs	https://doi.org/10.1007/978-3-319-31317-7_1
State	Published - 1 Jan 2016

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2016.

ASJC Scopus subject areas

General Mathematics

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10.1007/978-3-319-31317-7_1

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Applications of quasiconvexity

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