关于(h,m)-凸函数乘积的Hadamard-型不等式及应用

作者:孙文兵 刊名:中国科学院大学学报 上传者:孙红召

【摘要】建立一些关于(h,m)-凸函数乘积的新Hadamard-型不等式,得到的结果是对通常凸性、第2种意义下的s-凸性、m-凸性、h-凸性意义下的Hadamard-型不等式的推广.

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第35卷第2期 2018年 3月 中 国科 学 院 大 学 学 报 Journal of University of Chinese Academy of Sciences Vol|35 No.2 March 2018 文章编号:2095-6134(2018)02_0145_09 Hadamard.type inequalities for products of ( , ).convex functions and their applications SUN Wenbing (sc 。l of Scfe,批 ,Sh口oyang University,Sh口oyang 422000,Hulzan,Chin。) f Received 30 December 2016:Revised 13 April 2017) Had锄 ard.咖 e ineqlIali廿es f0r products of( ,m)-convex functions and their applications[J]·J。urnal。f uIli 。rsity of Chinese Academy of Sciences,2018,35(2):145-153· Abstract In this paper,we established some new Hadamard_type inequalities for Pr0ducts of( , m .c0nvex functions, which are the extended Hadamard—type inequalities for ordinary conVex ty sense,s—c。nvexity in the sec。nd sense,m-conVexity sense,and 一c。nVe ity 。呲 . Kevw0rds Hadamard’s inequality; convex functions; (h, m)。convex func ons;pr0duc 01 tw0 functions CLC number:0178 Document code:A doi:10.7523/j.issn.2095_6134·2018·02·001 关于(h, ).凸函数乘积的 Hadamard-型不等式及应用 孙文兵 (邵阳学院理学院,湖南 邵阳422000) 摘 要 建立一些关于( ,m).凸函数乘积的新Hadamard一型不等式,得到的结果是对通常凸 性、第2种意义下的s.凸性、m.凸性、h.凸性意义下的Hadamard_型不等式的推广· 关键词 Hadamard不等式;凸函数;( ,m)一凸函数;2个函数乘积 In recent years.the concept of convex functi。n has been extended by some scholars. For example, Breckner[ ]introduced the concept of s。convexity, and V盯0吾anec[2。defined h-convex functions. Some results for Hadamard—type inequalities related to the extended convex functions have been obtained 川 · In 2011.0zdemir et a1. p

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