(g,φh,m) - CONVEX AND (g, log φ) - CONVEX DOMINATED FUNCTIONS AND HADAMARD TYPE INEQUALITIES RELATED TO THEM.

In this paper, we present the notion of (g, φh,m) -convex and (g, log φ) -convex dominated function and present some properties of them. Besides, we attain some Hermite-Hadamard-type inequalities for (g, φh,m) -convex and (g, log φ) -convex dominated functions. Our results generalize some findings about Hermite-Hadamard-type inequalities in the literature. [ABSTRACT FROM AUTHOR]