k-FRACTIONAL OSTROWSKI TYPE INEQUALITIES VIA (s, r)-CONVEX

We introduce the 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 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 H & ouml;lder's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means are given.