凸函数的关于Riemann-Liouville分式积分的Hermite-Hadamard型不等式

2015-10-25 07:51白淑萍石德平谷桂花
关键词:淑萍通辽分式

白淑萍,石德平,谷桂花

(内蒙古民族大学数学学院,内蒙 古通辽 028043)

凸函数的关于Riemann-Liouville分式积分的Hermite-Hadamard型不等式

白淑萍,石德平,谷桂花

(内蒙古民族大学数学学院,内蒙古通辽028043)

凸函数的Hermite-Hadamard型不等式具有重要的理论意义,并且有着广泛的应用.首先建立了一个关于Riemann-Liouville分式积分的等式,然后讨论凸函数的关于Riemann-Liouville分式积分的Hermite-Hadamard型积分不等式,得到了若干个结果.

Riemann-Liouville分式积分;凸函数;Hermite-Hadamard型积分不等式

凸函数的Hermite-Hadamard型不等式具有重要的理论意义,并且有着广泛的应用.其相关的定义和定理如下:

定义1[1-2]设f:IR=(-∞,+∞)→R.若对任意的x,y∈I,t∈[0,1],有:

本文首先建立一个关于Riemann-Liouville分式积分的一个等式,然后讨论凸函数的关于Riemann-Liouville分式积分的Hermite-Hadamard型积分不等式.

1 一个引理

2 主要结果

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[7]SHI D P,XI B Y,QI F.Hermite--Hadamard type inequalities for Riemann-Liouville fractional integrals of(α,m)-convex functions[J].Fractional Differential Calculus,2014,4(2):33-43.

[8]SHI D P,XI B Y,QI F.Hermite--Hadamard type inequalities for(m,h1,h2)-convex functions via Riemann-Liouville fractional integrals[J]. Turkish Journal of Analysis and Number Theory,2014,2(1):22-27.

责任编辑:时 凌

Hermite-Hadamard Type Inequalities for Convex Functions Via Riemann-Liouville Fractional Integrals

BAI Shuping,SHI Deping,GU Guihua
(College of Mathematics,Inner Mongolia University for the Nationalities,Tongliao 028043,China)

Hermite-Hadamard type inequality of convex function has important theoretical significance,and has a wide range of applications.First,we establish a fractional integral equation with Riemann-Liouville.Then we discuss convex functions on Riemann-Liouville fractional integral of Hermite-Hadamard type integral inequality and obtain some results.

Riemann-Liouville fractional integral;convex function;Hermite-Hadamard type integral inequality

O159

A

1008-8423(2015)04-0384-04DOI:10.13501/j.cnki.42-1569/n.2015.12.007

2015-10-09.

内蒙古自治区高等学校科学研究项目(NJZY14192);内蒙古自治区自然科学研究项目(2015MS0123).

白淑萍(1967-),女,副教授,主要从事分析不等式的研究.

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