分形集上的广义调和s-凸函数及Hadamard型不等式  

Generalized Harmonically s-Convex Functions and Hadamard Type Inequalities on Fractal Sets

作　　者：孙文兵 SUN Wenbing(School of Science,Shaoyang University,Shaoyang 422000,Hunan Province,China)

机构地区：[1]邵阳学院理学院,湖南邵阳422000

出　　处：《吉林大学学报（理学版）》2018年第6期1366-1372,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:61672356);湖南省自然科学基金(批准号:12JJ3008);邵阳市科技计划项目(批准号:2017GX09)

摘　　要：在分形实线的分形集Rα(0<α≤1)上给出广义调和s-凸函数的定义,并建立关于广义调和s-凸函数的Hermite-Hadamard积分不等式以及关于局部分数阶积分的恒等式,进而得到了关于该类函数的几个Hermite-Hadamard型局部分数阶积分不等式.The author gave the definition of generalized harmonically s-convex function on fractal sets?α(0<α≤1)of fractalreal lines,established Hermite-Hadamard integral inequalities for generalizedharmonically s-convex function and an identity for local fractional integral.Then some Hermite-Hadamard type local fractional integral inequalities forthese classes of functions were obtained.

关 键 词：广义调和s-凸函数 Hermite-Hadamard型积分不等式 分形集 局部分数阶积分 

分 类 号：O178[理学—数学]