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 first presented some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-(r;m,p,q,h₁,h₂)-preinvex mappings. And then, a new identity concerning (n+1)-differentiable mappings defined on m-invex set via Caputo k-fractional derivatives 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 new estimates with respect to Ostrowski type inequalities via Caputo k-fractional derivatives are established. It is pointed out that some new special cases can be deduced from main results of the article.