Fejér type integral inequalities related with geometrically-arithmetically convex functions with applications

S. S. Dragomir; M. A. Latif; E. Momoniat

doi:10.12697/ACUTM.2019.23.05

Fejér type integral inequalities related with geometrically-arithmetically convex functions with applications

S. S. Dragomir, M. A. Latif, E. Momoniat

Mathematics and Applied Mathematics

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

8 Citations (Scopus)

Abstract

A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fejér type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the Hölder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.

Original language	English
Pages (from-to)	51-64
Number of pages	14
Journal	Acta et Commentationes Universitatis Tartuensis de Mathematica
Volume	23
Issue number	1
DOIs	https://doi.org/10.12697/ACUTM.2019.23.05
Publication status	Published - Jun 2019

Keywords

And phrases
Convex function
Fejér’s inequality
GA-convex function
Hadamard’s inequality
Hermite
Hölder’s inequality
Power mean inequality

ASJC Scopus subject areas

General Mathematics

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10.12697/ACUTM.2019.23.05

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abstract = "A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fej{\'e}r type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the H{\"o}lder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.",

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year = "2019",

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AU - Dragomir, S. S.

AU - Latif, M. A.

AU - Momoniat, E.

PY - 2019/6

Y1 - 2019/6

N2 - A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fejér type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the Hölder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.

AB - A new identity involving a geometrically symmetric function and a differentiable function is established. Some new Fejér type integral inequalities, connected with the left part of Hermite–Hadamard type inequalities for geometrically-arithmetically convex functions, are presented by using the Hölder integral inequality and the notion of geometrically-arithmetically convexity. Applications of our results to special means of positive real numbers are given.

KW - And phrases

KW - Convex function

KW - Fejér’s inequality

KW - GA-convex function

KW - Hadamard’s inequality

KW - Hermite

KW - Hölder’s inequality

KW - Power mean inequality

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SN - 1406-2283

VL - 23

SP - 51

EP - 64

JO - Acta et Commentationes Universitatis Tartuensis de Mathematica

JF - Acta et Commentationes Universitatis Tartuensis de Mathematica

IS - 1

ER -

Fejér type integral inequalities related with geometrically-arithmetically convex functions with applications

Abstract

Keywords

ASJC Scopus subject areas

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