Hermite-Hadamard-type inequalities for "Equation missing" -convex dominated functions

In this paper, we introduce the notion of ( g , φ h ) -convex dominated function and present some properties of them. Finally, we present a version of Hermite-Hadamard-type inequalities for ( g , φ h ) -convex dominated functions. Our results generalize the Hermite-Hadamard-type inequalities in Dragomir et al. (Tamsui Oxford Univ. J. Math. Sci. 18(2):161-173, 2002), Kavurmacı et al. (New Definitions and Theorems via Different Kinds of Convex Dominated Functions, 2012) and Özdemir et al. (Two new different kinds of convex dominated functions and inequalities via Hermite-Hadamard type, 2012). MSC: 26D15, 26D10, 05C38.