s-对数凸函数的Hermite-Hadamard型积分不等式

数学物理学报 ›› 2015, Vol. 35 ›› Issue (3): 515-524.

s-对数凸函数的Hermite-Hadamard型积分不等式

席博彦¹, 祁锋²

1. 内蒙古民族大学数学学院内蒙古通辽市 028043;
2. 天津工业大学理学院数学系天津市 300387

收稿日期:2013-08-01 修回日期:2014-11-15 出版日期:2015-06-25 发布日期:2015-06-25
作者简介:席博彦, baoyintu78@qq.com;祁锋, qifeng618@gmail.com
基金资助:
国家自然科学基金(11361038)和内蒙古自治区高等学校科学研究项目(NJZY14191)资助

Some Integral Inequalities of Hermite-Hadamard Type for s-Logarithmically Convex Functions

Xi Boyan¹, Qi Feng²

1. College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043;
2. Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300387

Received:2013-08-01 Revised:2014-11-15 Online:2015-06-25 Published:2015-06-25

摘要/Abstract

摘要：

该文定义了"s-对数凸函数"的概念, 并给出了可微s-对数凸函数的若干个 Hermite-Hadamard型积分不等式, 作为应用给出了平均数的几个不等式.

关键词: 积分不等式, 积分等式, Hermite-Hadamard积分不等式, 凸函数, s-对数凸函数

Abstract:

In the paper, we introduce the notion "s-logarithmically convex function", establish some new integral inequalities of Hermite-Hadamard type for functions the power of the absolute of whose first derivative is s-logarithmically convex, and apply these newly obtained inequalities to means.

Key words: Integral inequality, Integral identity, Hermite-Hadamard's integral inequality, Convex function, s-Logarithmically convex function

中图分类号:

O178

席博彦, 祁锋. s-对数凸函数的Hermite-Hadamard型积分不等式[J]. 数学物理学报, 2015, 35(3): 515-524.

Xi Boyan, Qi Feng. Some Integral Inequalities of Hermite-Hadamard Type for s-Logarithmically Convex Functions[J]. Acta mathematica scientia,Series A, 2015, 35(3): 515-524.

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