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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