Rearrangements and jensen type inequalities related to convexity, superquadracity, strong convexity and 1-quasiconvexity

S. Abramovich; L. E. Persson

doi:10.7153/jmi-2020-14-41

Rearrangements and jensen type inequalities related to convexity, superquadracity, strong convexity and 1-quasiconvexity

S. Abramovich, L. E. Persson

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we derive and discuss some new theorems related to all rearrangements of a given set in Rⁿ, denoted (x) and use the results to prove some new Jensen type inequalities for convex, superquadratic, strongly convex and 1-quasiconvex functions.

Original language	English
Pages (from-to)	641-659
Number of pages	19
Journal	Journal of Mathematical Inequalities
Volume	14
Issue number	3
DOIs	https://doi.org/10.7153/jmi-2020-14-41
State	Published - 1 Sep 2020

Bibliographical note

Publisher Copyright:
© 2020 Element D.O.O.

Keywords

Circular rearrangements
Convexity
Inequalities
Jensen's inequality
Rearrangements
Strong convexity, 1-quasiconvexity
Superquadracity

ASJC Scopus subject areas

Analysis

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10.7153/jmi-2020-14-41

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abstract = "In this paper we derive and discuss some new theorems related to all rearrangements of a given set in Rn, denoted (x) and use the results to prove some new Jensen type inequalities for convex, superquadratic, strongly convex and 1-quasiconvex functions.",

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KW - Convexity

KW - Inequalities

KW - Jensen's inequality

KW - Rearrangements

KW - Strong convexity, 1-quasiconvexity

KW - Superquadracity

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Rearrangements and jensen type inequalities related to convexity, superquadracity, strong convexity and 1-quasiconvexity

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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