Some fejér type integral inequalities for geometrically-arithmetically-convex functions with applications

Muhammad Amer Latif; Sever Silvestru Dragomir; Ebrahim Momoniat

doi:10.2298/FIL1806193L

Some fejér type integral inequalities for geometrically-arithmetically-convex functions with applications

Muhammad Amer Latif, Sever Silvestru Dragomir, Ebrahim Momoniat

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

22 Citations (Scopus)

Abstract

In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving geometrically symmetric functions is established, and by using the obtained identity, the Hölder integral inequality and the notion of geometrically-arithmetically convexity, some new Fejér type integral inequalities are presented. Applications of our results to special means of positive real numbers are given as well.

Original language	English
Pages (from-to)	2193-2206
Number of pages	14
Journal	Filomat
Volume	32
Issue number	6
DOIs	https://doi.org/10.2298/FIL1806193L
Publication status	Published - 2018
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.2298/FIL1806193L

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title = "Some fej{\'e}r type integral inequalities for geometrically-arithmetically-convex functions with applications",

abstract = "In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving geometrically symmetric functions is established, and by using the obtained identity, the H{\"o}lder integral inequality and the notion of geometrically-arithmetically convexity, some new Fej{\'e}r type integral inequalities are presented. Applications of our results to special means of positive real numbers are given as well.",

keywords = "Convex function, Fej{\'e}r{\textquoteright}s inequality, GA-convex function, Hermite-Hadamard{\textquoteright}s inequality, H{\"o}lder{\textquoteright}s inequality, Power mean inequality",

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year = "2018",

doi = "10.2298/FIL1806193L",

language = "English",

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AU - Latif, Muhammad Amer

AU - Dragomir, Sever Silvestru

AU - Momoniat, Ebrahim

PY - 2018

Y1 - 2018

N2 - In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving geometrically symmetric functions is established, and by using the obtained identity, the Hölder integral inequality and the notion of geometrically-arithmetically convexity, some new Fejér type integral inequalities are presented. Applications of our results to special means of positive real numbers are given as well.

AB - In this paper, the notion of geometrically symmetric functions is introduced. A new identity involving geometrically symmetric functions is established, and by using the obtained identity, the Hölder integral inequality and the notion of geometrically-arithmetically convexity, some new Fejér type integral inequalities are presented. Applications of our results to special means of positive real numbers are given as well.

KW - Convex function

KW - Fejér’s inequality

KW - GA-convex function

KW - Hermite-Hadamard’s inequality

KW - Hölder’s inequality

KW - Power mean inequality

UR - https://www.scopus.com/pages/publications/85061347285

U2 - 10.2298/FIL1806193L

DO - 10.2298/FIL1806193L

M3 - Article

AN - SCOPUS:85061347285

SN - 0354-5180

VL - 32

SP - 2193

EP - 2206

JO - Filomat

JF - Filomat

IS - 6

ER -

Some fejér type integral inequalities for geometrically-arithmetically-convex functions with applications

Abstract

Keywords

ASJC Scopus subject areas

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