一类(α,m)-凸函数的Hadamard 型不等式

doi:10.12066/j.issn.1007-2861.1716

上海大学学报(自然科学版) ›› 2017, Vol. 23 ›› Issue (4): 583-589.doi: 10.12066/j.issn.1007-2861.1716

一类(α,m)-凸函数的Hadamard 型不等式

李玉娇¹, 杜廷松^1,2

1. 三峡大学理学院, 湖北宜昌 443002;
2. 武汉科技大学冶金工业过程系统科学湖北省重点实验室, 武汉 430081

收稿日期:2015-06-01 出版日期:2017-08-30 发布日期:2017-08-30
通讯作者: 杜廷松(1969—), 男, 教授, 研究方向为凸分析及最优化理论与算法. E-mail: tingsongdu@ctgu.edu.cn
作者简介:杜廷松(1969—), 男, 教授, 研究方向为凸分析及最优化理论与算法. E-mail: tingsongdu@ctgu.edu.cn
基金资助:
国家自然科学基金资助项目(61374028); 湖北省自然科学基金资助项目(2013CFA131); 三峡大学培优基金资助项目(2015PY075)

Hadamard-type inequalities for a class of (α ,m)-convex functions

LI Yujiao¹, DU Tingsong^1,2

1. College of Science, China Three Gorges University, Yichang 443002, Hubei, China;
2. Hubei Province Key Laboratory of System Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430081, China

Received:2015-06-01 Online:2017-08-30 Published:2017-08-30

摘要/Abstract

摘要：

首先, 提出了一个新的积分恒等式; 然后, 在此基础上构造了一类二阶导函数的绝对值的q次幂是(α,m)-凸函数的新型Hadamard 型不等式; 最后, 给出了一些具体的应用例子.

关键词: (α,m)-凸函数, Hadamard 型不等式, 凸函数

Abstract:

This paper proposes an integral identity. Based on the identity, some results of Hadamard inequalities are established for functions with the q-th power of the second derivative’s absolute value (α,m)-convex. Some specific applied examples are presented.

Key words: Hadamard-type inequality, (α, m)-convex function, convex function

李玉娇1, 杜廷松1,2. 一类(α,m)-凸函数的Hadamard 型不等式[J]. 上海大学学报(自然科学版), 2017, 23(4): 583-589.

LI Yujiao1, DU Tingsong1,2. Hadamard-type inequalities for a class of (α ,m)-convex functions[J]. Journal of Shanghai University（Natural Science Edition）, 2017, 23(4): 583-589.

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一类(α,m)-凸函数的Hadamard 型不等式

Hadamard-type inequalities for a class of (α ,m)-convex functions

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