SOME CAPUTO k-FRACTIONAL DERIVATIVES OF OSTROWSKI TYPE CONCERNING (n + 1)-DIFFERENTIABLE GENERALIZED RELATIVE SEMI-(r; m; p; q; h1; h2)-PREINVEX MAPPINGS

Abstract

In this article, we Örst presented some integral inequalities forGauss-Jacobi type quadrature formula involving generalized relative semi-(r; m; p; q; h1; h2)-preinvex mappings. And then, a new identity concerning(n + 1)-di§erentiable mappings deÖned on m-invex set via Caputo k-fractionalderivatives is derived. By using the notion of generalized relative semi-(r; m; p; q;h1; h2)-preinvexity and the obtained identity as an auxiliary result, some newestimates with respect to Ostrowski type inequalities via Caputo k-fractionalderivatives are established. It is pointed out that some new special cases canbe deduced from main results of the article.