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].

引用

页码：87 / 100

页数：14

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