A NEW HERMITE-HADAMARD-TYPE INEQUALITY AND ITS APPLICATION TO QUASI-EINSTEIN METRICS

摘要

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.