Some weighted integral inequalities for differentiable h-preinvex functions

被引：7

作者：

Latif, Muhammad Amer ^{[1
]}

Dragomir, Sever Silvestru ^{[2
,3
]}

Momoniat, Ebrahim ^{[1
]}

机构：

[1] Univ Witwatersrand, Sch Comp Sci & Appl Math, Private Bag 3, ZA-2050 Johannesburg, South Africa

[2] Victoria Univ, Coll Engn & Sci, Math, POB 14428, Melbourne, MC 8001, Australia

[3] Univ Witwatersrand, Sch Computat & Appl Math, Private Bag 3, ZA-2050 Johannesburg, South Africa

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2018年 / 25卷 / 03期

关键词：

Hermite-Hadamard's inequality; invex set; preinvex function; h-preinvex function; Holder's integral inequality; power-mean inequality; HADAMARD TYPE INEQUALITIES; REAL NUMBERS; ABSOLUTE VALUE; MAPPINGS; CONVEX;

D O I：

10.1515/gmj-2016-0081

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Holder 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.

引用

页码：441 / 450

页数：10

共 34 条

[1] A superadditive property of Hadamard's gamma function [J].