MM-convex function & its Jensen-type inequality(MM-凸函数及其Jensen型不等式)

SONGZhenyun(宋振云); CHENShaoyuan(陈少元); HUFugao(胡付高)

doi:10.3785/j.issn.1008-9497.2017.04.004

Zhejiang Daxue xuebao. Lixue ban (Jul 2017)

MM-convex function & its Jensen-type inequality(MM-凸函数及其Jensen型不等式)

SONGZhenyun(宋振云),
CHENShaoyuan(陈少元),
HUFugao(胡付高)

Affiliations

SONGZhenyun(宋振云): ORCiD; 1.School of Mechanical & Electrical Engineering, Hubei Polytechnic Institute, Xiaogan 432000, Hubei Province, China( 1.湖北职业技术学院机电工程学院，湖北孝感 432000)
CHENShaoyuan(陈少元): 1.School of Mechanical & Electrical Engineering, Hubei Polytechnic Institute, Xiaogan 432000, Hubei Province, China( 1.湖北职业技术学院机电工程学院，湖北孝感 432000)
HUFugao(胡付高): 2.School of Mathematics & Statistics, Hubei Engineering University, Xiaogan 432000, Hubei Province, China( 2.湖北工程学院数学与统计学院，湖北孝感 432000)

DOI: https://doi.org/10.3785/j.issn.1008-9497.2017.04.004
Journal volume & issue: Vol. 44, no. 4
pp. 403 – 410

Abstract

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考虑函数的广义凸性问题，利用区间上的二元幂平均定义了MM-凸函数，讨论了MM-凸函数的若干判定定理及运算性质，建立了其Jensen型不等式，并给出了Jensen型不等式的等价形式及推论.结果表明，MM-凸函数是比较函数定义区间内任意两点的幂平均函数值与其函数值的幂平均大小所确定的各类凸函数的推广.MM-凸函数概念的引入，为深入研究凸函数和拓展凸函数概念探索了一条新途径.

Published in Zhejiang Daxue xuebao. Lixue ban

ISSN: 1008-9497 (Print)
Publisher: Zhejiang University Press
Country of publisher: China
LCC subjects: Science: Mathematics: Instruments and machines: Electronic computers. Computer science; Science: Physics
Website: https://www.zjujournals.com/sci/EN/1008-9497/home.shtml

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