Some New Hermite–Hadamard Type Integral Inequalities for Twice Differentiable Generalized ((h 1, h 2); (η 1, η 2))-Convex Mappings and Their Applications

Abstract

In this article, we first introduced a new class of generalized ((h1, h2);(η1, η2))-convex mappings and an interesting lemma regarding Hermite–Hadamard type integral inequalities. By using the notion of generalized ((h1, h2);(η1, η2))-convexity and lemma as an auxiliary result, some new estimates difference between the left and middle part in Hermite–Hadamard type integral inequality associated with twice differentiable generalized ((h1, h2);(η1, η2))-convex mappings are established. It is pointed out that some new special cases can be deduced from main results. At the end, some applications to special means for different positive real numbers are provided.