K-fractional Ostrowski type inequalities via (s, r)-conex

Abstract

We are introducing very first time a generalized class named it the class of (s, r)-convex in mixed kind, this class includes s-convex in 1st and 2nd kind, P-convex, quasi-convex, and the class of ordinary convex. Also, we would like to state the generalization of the classical Ostrowski inequality via k-fractional integrals, which is obtained for functions whose first derivative in absolute values is (s, r)-convex in mixed kind. Moreover, we establish some Ostrowski type inequalities via k-fractional integrals and their particular cases for the class of functions whose absolute values at certain powers of derivatives are (s, r)-convex in mixed kind by using different techniques including Holder's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given.