On new inequalities of Hermite-Hadamard-Fejer type for harmonically convex functions via fractional integrals

Mehmet Kunt; İmdat İşcan; Nazlı Yazıcı; Uğur Gözütok

doi:10.1186/s40064-016-2215-4

On new inequalities of Hermite-Hadamard-Fejer type for harmonically convex functions via fractional integrals

Springerplus. 2016 May 17:5:635. doi: 10.1186/s40064-016-2215-4. eCollection 2016.

Authors

Mehmet Kunt¹, İmdat İşcan², Nazlı Yazıcı¹, Uğur Gözütok¹

Affiliations

¹ Department of Mathematics, Faculty of Sciences, Karadeniz Technical University, Trabzon, Turkey.
² Department of Mathematics, Faculty of Sciences and Arts, Giresun University, Giresun, Turkey.

Abstract

In this paper, firstly, new Hermite-Hadamard type inequalities for harmonically convex functions in fractional integral forms are given. Secondly, Hermite-Hadamard-Fejer inequalities for harmonically convex functions in fractional integral forms are built. Finally, an integral identity and some Hermite-Hadamard-Fejer type integral inequalities for harmonically convex functions in fractional integral forms are obtained. Some results presented here provide extensions of others given in earlier works.

Keywords: Harmonically convex functions; Hermite–Hadamard inequality; Hermite–Hadamard–Fejer inequality; Riemann–Liouville fractional integrals.