分形空间上广义凸函数的新Simpson型不等式及应用  

New Simpson Type Inequalities for Generalized Convex Functions on Fractal Space and Its Applications

作　　者：孙文兵 刘琼 Sun Wenbing;Liu Qiong(School of Science,Shaoyang University,Hunan Shaoyang 422000)

机构地区：[1]邵阳学院理学院,湖南邵阳422000

出　　处：《数学物理学报（A辑）》2018年第6期1058-1066,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(61672356);邵阳市科技计划项目(2017GX09)~~

摘　　要：根据局部分数阶微积分理论以及分形实线的α(0 <α≤1)型集合R~α上广义凸函数的定义,获得了几个涉及局部分数阶积分的Simpson型不等式.最后,给出了所得不等式在特殊均值和数值积分中的几个应用.In the paper,the authors use local fractional calculus theory and the definition of generalized convex function on the a type set of the real line numbers Ra,some new Simpson-type inequalities involving local fractional integrals are established.Finally,some applications of our obtained inequalities to special means and numerical integration are given.

关 键 词：Simpson型不等式 广义凸函数 局部分数阶导数 局部分数阶积分 

分 类 号：O178[理学—数学]