SOME GENERALIZED HERMITE-HADAMARD TYPE INEQUALITIES INVOLVING FRACTIONAL INTEGRAL OPERATOR FOR FUNCTIONS WHOSE SECOND DERIVATIVES IN ABSOLUTE VALUE ARE S-CONVEX

被引：0
|
作者：
Set, E. [1 ]
Dragomir, S. S. [2 ]
Gozpinar, A. [1 ]
机构：
[1] Ordu Univ, Fac Sci & Arts, Dept Math, Ordu, Turkey
[2] Victoria Univ, Coll Engn & Sci, Math, Melbourne, Vic, Australia
来源：
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE | 2019年 / 88卷 / 01期
关键词：
Hermite-Hadamard inequality; convex function; Holder inequality; Riemann-Liouville fractional integral; fractional integral operator;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, a general integral identity for twice differentiable mapping involving fractional integral operators is derived. Secondly by using this identity we obtain some new generalized Hermite-Hadamards type inequalities for functions whose absolute values of second derivatives are s-convex and concave. The main results generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liouville fractional integral. Also we point out, some results in this study in some special cases such as setting s = 1, lambda = alpha, sigma (0) = 1 and w = 0, more reasonable than those obtained in [8].
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收藏
页码：87 / 100
页数：14
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