Generalization and reverses of the left Fejer inequality for convex functions

被引：0
作者：
Dragomir, S. S. [1 ,2 ]
机构：
[1] Victoria Univ, Math Sch Engn & Sci, POB 14428, Melbourne, MC 8001, Australia
[2] Univ Witwatersrand, Sch Computat & Appl Math, Private Bag 3, ZA-2050 Johannesburg, South Africa
来源：
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | 2017年 / 10卷 / 06期
关键词：
Convex functions; integral inequalities; Jensen's type inequalities; Fejer type inequalities; Lebesgue integral; Hermite-Hadamard type inequalities; special means; INTEGRAL-INEQUALITIES; HADAMARD-TYPE;
D O I：
10.22436/jnsa.010.06.35
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we establish a generalization of the left Fejer inequality for general Lebesgue integral on measurable spaces as well as various upper bounds for the difference 1/integral(b)(a) g (x) dx integral(b)(a) h(x) g (x) dx - h (a+b/2), where h : [a, b] -> R is a convex function and g : [a, b] -> [0, infinity) is an integrable weight. Applications for discrete means and Hermite-Hadamard type inequalities are also provided. (C) 2017 All rights reserved.
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页码：3231 / 3244
页数：14
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