A New Hermite–Hadamard-Type Inequality and its Application to Quasi-Einstein Metrics

Abstract

We first establish a new generalization of the classical Hermite–Hadamard inequality for a real-valued convex function. Then the convexity of the matrix function g(A) = f(det A) is proved under certain conditions imposed on the function f and the matrix A: On this basis, we deduce a new Hermite–Hadamard-type inequality and finally present an application to the estimation of the volume of quasi-Einstein metrics.