Hermite-Hadamard type inequalities for F-convex function involving fractional integrals

Pshtiwan Othman Mohammed; Mehmet Zeki Sarikaya

doi:10.1186/s13660-018-1950-1

Hermite-Hadamard type inequalities for F-convex function involving fractional integrals

J Inequal Appl. 2018;2018(1):359. doi: 10.1186/s13660-018-1950-1. Epub 2018 Dec 29.

Authors

Pshtiwan Othman Mohammed¹, Mehmet Zeki Sarikaya²

Affiliations

¹ 1Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Iraq.
² 2Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey.

Abstract

In this study, the family F and F-convex function are given with its properties. In view of this, we establish some new inequalities of Hermite-Hadamard type for differentiable function. Moreover, we establish some trapezoid type inequalities for functions whose second derivatives in absolute values are F-convex. We also show that through the notion of F-convex we can find some new Hermite-Hadamard type and trapezoid type inequalities for the Riemann-Liouville fractional integrals and classical integrals.

Keywords: λ φ -preinvex; F-convex; Integral inequalities.