On Dominated Classes of Harmonic Convex Functions and Associated Integral Inequalities

Abstract

In this article, we introduce and investigate dominated classes the notion of (h,g)-harmonic convex dominated functions. As particular cases of (h,g)-harmonic convex dominated functions, we also define some other new classes of harmonic convex dominated. We derive some integral inequalities of Hermite-Hadamard type via (h,g)-harmonic convex dominated functions and also give the fractional version of these inequalities. Some new special cases are also discussed which can be deduced from our main results.

Key words and phrases. h-convex functions, harmonically convex functions, (h,g)-harmonic convex dominated functions, Hermite-Hadamard, inequalities.

2000 Mathematics Subject Classification. 26A33, 26D07, 26D10, 26D15