@article{article_501430, title={SOME CAPUTO k-FRACTIONAL DERIVATIVES OF OSTROWSKI TYPE CONCERNING (n + 1)-DIFFERENTIABLE GENERALIZED RELATIVE SEMI-(r; m; p; q; h1; h2)-PREINVEX MAPPINGS}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={68}, pages={973–996}, year={2019}, DOI={10.31801/cfsuasmas.501430}, author={Kashuri, Artion and Liko, Rozana}, keywords={Ostrowski type inequality, Hölder’s inequality, Minkowski inequality, power mean inequality, Caputo k-fractional derivatives, s-convex function in the second sense, m-invex}, abstract={<div>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, <span style="font-size:.9em;">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. </span> </div>}, number={1}, publisher={Ankara University}