Some Caputo K-Fractional Derivatives of Ostrowski Type Concerning (n + 1)-Differentiable Generalized Relative Semi-(r; m; p; q; h1; h2)-Preinvex Mappings
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Date
2019-02-01
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Ankara Üniversitesi Fen Fakültesi
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.
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Ostrowski type inequality, Hölder's inequality, Minkowski inequality