Hermite-Hadamard like inequalities for fractional integral operator via convexity and quasi-convexity with their applications

Abstract

Since the supposed Hermite-Hadamard inequality for a convex function was discussed, its expansions, refinements, and variations, which are called Hermite-Hadamard type inequalities, have been widely explored. The main objective of this article is to acquire new Hermite-Hadamard type inequalities employing the Riemann-Liouville fractional operator for functions whose third derivatives of absolute values are convex and quasi-convex in nature. Some special cases of the newly presented results are discussed as well. As applications, several estimates concerning Bessel functions and special means of real numbers are illustrated.

Keywords

• convexity
• quasi-convexity
• hermite-hadamard inequality
• hölder's rogers inequality
• young's inequality
• power mean inequality