| 时统业,李鼎,李军.与GM凸函数有关的若干积分不等式[J].井冈山大学自然版,2017,(3):13-18 |
| 与GM凸函数有关的若干积分不等式 |
| INTEGRAL INEQUALITIES RELATED TO GM-CONVEX FUNCTIONS |
| 投稿时间：2016-10-13 修订日期：2017-03-02 |
| DOI：10.3969/j.issn.1674-8085.2017.03.003 |
| 中文关键词: GM凸函数 GA凸函数 积分不等式 |
| 英文关键词: GM-convex function GA-convex function integral inequality |
| 基金项目: |
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| 摘要点击次数: 1729 |
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| 中文摘要: |
| 利用GM凸函数与GA凸函数的关系，证明了GM凸函数存在单侧导数，并通过不等式建立了GM凸函数与其单侧导数的联系。给出GA凸函数的左（右）导数积分的计算公式。用普通数学分析的方法建立了若干GM凸函数的积分不等式。 |
| 英文摘要: |
| With the aid of the relationship between GM-convex functions and GA-convex functions,the existence of unilateral derivatives of GM-convex functions is proved,and the relation between GM-convex function and its unilateral derivative is established through inequalities. Calculating formulas of left or right derivative integration of GA-convex function are given. Integral inequalities for GM-convex functions are obtained by using mathematical analysis. |
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