Generalised Hermite-Hadamard type inequalities for ( s , r ) -convex functions in mixed kind with applications

Abstract

In this article, some generalized inequalities of the Hermite-Hadamard type for functions whose modulus of the derivatives are \((s,r)\)-convex in mixed kind and applications for probability theory and numerical integration are given. Various established results of different articles would be recaptured as special cases. We also provide special cases of the class of \((s,r)\)-convex function on several choices of \(s,r\).