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

Year 2019, Volume: 68 Issue: 1, 973 - 996, 01.02.2019

Artion Kashuri , Rozana Liko

https://doi.org/10.31801/cfsuasmas.501430

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.

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

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