Generalized Hermite-Hadamard type inequalities involving fractional integral operators

Erhan Set; Muhammed Aslam Noor; Muhammed Uzair Awan; Abdurrahman Gözpinar

doi:10.1186/s13660-017-1444-6

Generalized Hermite-Hadamard type inequalities involving fractional integral operators

J Inequal Appl. 2017;2017(1):169. doi: 10.1186/s13660-017-1444-6. Epub 2017 Jul 19.

Authors

Erhan Set¹, Muhammed Aslam Noor^{2

3}, Muhammed Uzair Awan⁴, Abdurrahman Gözpinar¹

Affiliations

¹ Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey.
² Department of Mathematics, King Saud University, Riyadh, Saudi Arabia.
³ Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan.
⁴ Department of Mathematics, Government College University, Faisalabad, Pakistan.

Abstract

In this article, a new general integral identity involving generalized fractional integral operators is established. With the help of this identity new Hermite-Hadamard type inequalities are obtained for functions whose absolute values of derivatives are convex. As a consequence, the main results of this paper generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liouville fractional integral.

Keywords: Hermite-Hadamard inequality; Hölder inequality; convex function; fractional integral operator.