Some weighted integral inequalities for differentiable h-preinvex functions

Muhammad Amer Latif; Sever Silvestru Dragomir; Ebrahim Momoniat

doi:10.1515/gmj-2016-0081

Some weighted integral inequalities for differentiable h-preinvex functions

Muhammad Amer Latif, Sever Silvestru Dragomir, Ebrahim Momoniat

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

5 Citations (Scopus)

Abstract

In this paper, by using a weighted identity for functions defined on an open invex subset of the set of real numbers, by using the Hölder integral inequality and by using the notion of h-preinvexity, we present weighted integral inequalities of Hermite-Hadamard-type for functions whose derivatives in absolute value raised to certain powers are h-preinvex functions. Some new Hermite-Hadamard-type integral inequalities are obtained when h is super-additive. Inequalities of Hermite-Hadamard-type for s-preinvex functions are given as well as a special case of our results.

Original language	English
Pages (from-to)	441-450
Number of pages	10
Journal	Georgian Mathematical Journal
Volume	25
Issue number	3
DOIs	https://doi.org/10.1515/gmj-2016-0081
Publication status	Published - 1 Sept 2018
Externally published	Yes

Keywords

Hermite-Hadamard's inequality
Hölder's integral inequality
h-preinvex function
invex set
power-mean inequality
preinvex function

ASJC Scopus subject areas

General Mathematics

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10.1515/gmj-2016-0081

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title = "Some weighted integral inequalities for differentiable h-preinvex functions",

abstract = "In this paper, by using a weighted identity for functions defined on an open invex subset of the set of real numbers, by using the H{\"o}lder integral inequality and by using the notion of h-preinvexity, we present weighted integral inequalities of Hermite-Hadamard-type for functions whose derivatives in absolute value raised to certain powers are h-preinvex functions. Some new Hermite-Hadamard-type integral inequalities are obtained when h is super-additive. Inequalities of Hermite-Hadamard-type for s-preinvex functions are given as well as a special case of our results.",

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AU - Latif, Muhammad Amer

AU - Dragomir, Sever Silvestru

AU - Momoniat, Ebrahim

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N2 - In this paper, by using a weighted identity for functions defined on an open invex subset of the set of real numbers, by using the Hölder integral inequality and by using the notion of h-preinvexity, we present weighted integral inequalities of Hermite-Hadamard-type for functions whose derivatives in absolute value raised to certain powers are h-preinvex functions. Some new Hermite-Hadamard-type integral inequalities are obtained when h is super-additive. Inequalities of Hermite-Hadamard-type for s-preinvex functions are given as well as a special case of our results.

AB - In this paper, by using a weighted identity for functions defined on an open invex subset of the set of real numbers, by using the Hölder integral inequality and by using the notion of h-preinvexity, we present weighted integral inequalities of Hermite-Hadamard-type for functions whose derivatives in absolute value raised to certain powers are h-preinvex functions. Some new Hermite-Hadamard-type integral inequalities are obtained when h is super-additive. Inequalities of Hermite-Hadamard-type for s-preinvex functions are given as well as a special case of our results.

KW - Hermite-Hadamard's inequality

KW - Hölder's integral inequality

KW - h-preinvex function

KW - invex set

KW - power-mean inequality

KW - preinvex function

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DO - 10.1515/gmj-2016-0081

M3 - Article

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SP - 441

EP - 450

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

IS - 3

ER -

Some weighted integral inequalities for differentiable h-preinvex functions

Abstract

Keywords

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