Some New Hermite-Hadamard-Fejer Type Inequlaties via k-Fractional Integrals Concerning Differentiable Generalized Relative Semi-(r; m, h1, h2)-Preinvex Mappings

Miftar Ramosacaj, Artion Kashuri, Rozana Liko

Abstract

In this article, we first presented a new identity concerning differentiable mappings defined on m-invex set via k-fractional integrals. By using the notion of generalized relative semi-(r;m,h1,h2)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard-Fejer type inequalities via k-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

Keywords

Hermite-Hadamard inequality; Hermite-Hadamard-Fejer inequality; Holder's inequality; Minkowski inequality; power mean inequality; k-fractional integrals; m-invex

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