k-fractional Ostrowski type inequalities via (s, r)-convex

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 1(st )and 2(nd) 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 Ho & BULL;lder's inequality and power mean in-equality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given.