Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals

Praveen Agarwal; Mohamed Jleli; Muharrem Tomar

doi:10.1186/s13660-017-1318-y

Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals

J Inequal Appl. 2017;2017(1):55. doi: 10.1186/s13660-017-1318-y. Epub 2017 Mar 4.

Authors

Praveen Agarwal¹, Mohamed Jleli², Muharrem Tomar³

Affiliations

¹ Department of Mathematics, Anand International College of Engineering, Jaipur, 303012 India.
² Department of Mathematics, King Saud University, Riyadh, 11451 Kingdom of Saudi Arabia.
³ Department of Mathematics, Faculty of Arts and Sciences, Ordu University, Ordu, 52200 Turkey.

Abstract

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named [Formula: see text]-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

Keywords: Hermite-Hadamard inequality; [Formula: see text]-Riemann-Liouville fractional integral; [Formula: see text]-fractional integral; generalized k-fractional integral.