On γ-quasiconvexity, superquadracity and two-sided reversed jensen type inequalities

S. Abramovich; L. E. Persson; N. Samko

doi:10.7153/mia-18-46

On γ-quasiconvexity, superquadracity and two-sided reversed jensen type inequalities

S. Abramovich, L. E. Persson, N. Samko

Department of Mathematics

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

Abstract

In this paper we deal with γ-quasiconvex functions when -1≤γ ≤ 0, to derive some two-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalities for 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functions with Jensen type inequalities for superquadratic functions and we extend the result obtained for γ -quasiconvex functions to more general classes of functions.

Original language	English
Pages (from-to)	615-627
Number of pages	13
Journal	Mathematical Inequalities and Applications
Volume	18
Issue number	2
DOIs	https://doi.org/10.7153/mia-18-46
State	Published - 1 Apr 2015

Keywords

Convex functions
Refined Jensen type inequalities
Superquadratic functions
γ-quasiconvex functions

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.7153/mia-18-46

Cite this

@article{fe123b7bae72418898a7f8a640ac6b5e,

title = "On γ-quasiconvexity, superquadracity and two-sided reversed jensen type inequalities",

abstract = "In this paper we deal with γ-quasiconvex functions when -1≤γ ≤ 0, to derive some two-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalities for 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functions with Jensen type inequalities for superquadratic functions and we extend the result obtained for γ -quasiconvex functions to more general classes of functions.",

keywords = "Convex functions, Refined Jensen type inequalities, Superquadratic functions, γ-quasiconvex functions",

author = "S. Abramovich and Persson, {L. E.} and N. Samko",

year = "2015",

month = apr,

day = "1",

doi = "10.7153/mia-18-46",

language = "English",

volume = "18",

pages = "615--627",

journal = "Mathematical Inequalities and Applications",

issn = "1331-4343",

publisher = "Element d.o.o.",

number = "2",

}

TY - JOUR

T1 - On γ-quasiconvexity, superquadracity and two-sided reversed jensen type inequalities

AU - Abramovich, S.

AU - Persson, L. E.

AU - Samko, N.

PY - 2015/4/1

Y1 - 2015/4/1

N2 - In this paper we deal with γ-quasiconvex functions when -1≤γ ≤ 0, to derive some two-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalities for 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functions with Jensen type inequalities for superquadratic functions and we extend the result obtained for γ -quasiconvex functions to more general classes of functions.

AB - In this paper we deal with γ-quasiconvex functions when -1≤γ ≤ 0, to derive some two-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalities for 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functions with Jensen type inequalities for superquadratic functions and we extend the result obtained for γ -quasiconvex functions to more general classes of functions.

KW - Convex functions

KW - Refined Jensen type inequalities

KW - Superquadratic functions

KW - γ-quasiconvex functions

UR - http://www.scopus.com/inward/record.url?scp=84946169549&partnerID=8YFLogxK

U2 - 10.7153/mia-18-46

DO - 10.7153/mia-18-46

M3 - Article

AN - SCOPUS:84946169549

SN - 1331-4343

VL - 18

SP - 615

EP - 627

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

IS - 2

ER -

On γ-quasiconvexity, superquadracity and two-sided reversed jensen type inequalities

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this