Trapezium-Type Inequalities for an Extension of Riemann–Liouville Fractional Integrals Using Raina’s Special Function and Generalized Coordinate Convex Functions

Abstract

In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite–Hadamard inequality for generalized coordinate ϕ-convex functions via an extension of the Riemann–Liouville fractional integral. Furthermore, an interesting identity for functions with two variables is obtained, and with the use of it, some new extensions of trapezium-type inequalities using Raina’s special function via generalized coordinate ϕ-convex functions are developed. Various special cases have been studied. At the end, a brief conclusion is given as well.

Keywords

• trapezium-type inequality
• generalized convexity
• special functions