Some new Hermite-Hadamard type inequalities via k-fractional integrals concerning differentiable generalized relative semi-(r; m, p, q, h1 , h2)-preinvex mappings

Artion Kashuri; Rozana Liko

doi:10.1515/fascmath-2018-0004

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Title

Some new Hermite-Hadamard type inequalities via k-fractional integrals concerning differentiable generalized relative semi-(r; m, p, q, h1 , h2)-preinvex mappings

Authors

Year of publication

2018

Published in

Fasciculi Mathematici

Journal year: 2018 | Journal number: nr 60

Article type

scientific article

Publication language

english

Keywords

EN

Hermite-Hadamard type inequality
Hölder's inequality
Minkowski inequality
power mean inequality
k-fractional integrals
m-invex

Abstract

EN 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, p, q, h₁, h₂ )-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard 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.