2<i>D</i> approximately reciprocal <i>ρ</i>-convex functions and associated integral inequalities

Abstract

The main objective of this article is to introduce the notion of 2<i>D</i> approximately reciprocal <i>ρ</i>-convex functions, show that this class of functions unifies several other unrelated classes of reciprocal convex functions, obtain several new refinements of the Hermite-Hadamard type inequalities involving 2<i>D</i> approximately reciprocal <i>ρ</i>-convex functions, provide some bounds pertaining to the trapezium like inequalities by using partial differentiable 2<i>D</i> approximately reciprocal <i>ρ</i>-convex functions, and discuss the special cases of the obtained results.