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

Authors : Artion KASHURİ, Rozana LİKO

Pages : 973-996

Doi:10.31801/cfsuasmas.501430

View : 43 | Download : 12

Publication Date : 2019-02-01

Article Type : Research Paper

Abstract :In this article, we first presented some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-insert ignore into journalissuearticles values(r;m,p,q,h₁,h₂);-preinvex mappings. And then, a new identity concerning insert ignore into journalissuearticles values(n+1);-differentiable mappings defined on m-invex set via Caputo k-fractional derivatives is derived. By using the notion of generalized relative semi-insert ignore into journalissuearticles values(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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