On Generalization of Trapezoid Type Inequalities for s-Convex Functions with Generalized Fractional Integral Operators

Abstract

By using contemporary theory of inequalities, this study is devoted topropose a number of refinements inequalities for the Hermite$-$Hadamard'stype inequality and conclude explicit bounds for the trapezoid inequalitiesin terms of $s$-convex mappings, at most second derivative through theinstrument of generalized fractional integral operator and a considerableamount of results for special means. The results of this study which are thegeneralization of those given in earlier works are obtained for functions $f$where $|f^{\prime }|$ and $|f^{\prime \prime }|$ (or $|f^{\prime }|^{q}$ and $|f^{\prime \prime }|^{q}$ for $q\geq 1$) are $s$-convex hold by applyingthe Holder inequality and the power mean inequality.