Extension of Hermite-Hadamard Type Integral Inequality Whose Second Order Derivatives are m- Convex Functions

Abstract

Integral inequality is a fascinating research domain that helps to estimate the integral mean of convex functions. The convexity theory plays a basic role in the development of various branches of applied sciences. Convexity and inequality are connected which has a fundamental character in many branches of pure and applied disciplines. The Hermite-Hadamard (H-H) type integral inequality is one of the most important inequalities associated with the convex functions. The researchers are being motivated to the extensions, enhancements and generalizations of H-H type inequality for different types of convex functions. In this paper, we have obtained an extension of some integral inequalities of Hermite-Hadamard type for m-convex functions with second order derivatives on the basis of the classical convex functions.