Hermite-Hadamard-type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity

被引：96
|
作者：
Wang, JinRong [1 ]
Li, Xuezhu [1 ]
Feckan, Michal [2 ]
Zhou, Yong [3 ]
机构：
[1] Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China
[2] Comenius Univ, Dept Math Anal & Numer Math, Fac Math Phys & Informat, Bratislava 84248, Slovakia
[3] Xiangtan Univ, Dept Math, Xiangtan 411105, Hunan, Peoples R China
来源：
APPLICABLE ANALYSIS | 2013年 / 92卷 / 11期
关键词：
m-convex functions; (s; m)-convex functions; Hermite-Hadamard-type inequalities; Riemann-Liouville fractional integrals; 26A33; 26A51; 26D15; (ALPHA;
D O I：
10.1080/00036811.2012.727986
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, two fundamental integral identities including the second-order derivatives of a given function via Riemann-Liouville fractional integrals are established. With the help of these two fractional-type integral identities, all kinds of Hermite-Hadamard-type inequalities involving left-sided and right-sided Riemann-Liouville fractional integrals for m-convex and (s,m)-convex functions, respectively. Our methods considered here may be a stimulant for further investigations concerning Hermite-Hadamard-type inequalities involving Hadamard fractional integrals.
引用
收藏
页码：2241 / 2253
页数：13
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