Strong Schur-Convexity of the Integral Mean

摘要

The strong Schur-convexity of the integral mean as well as of the left and right gaps in the Hermite-Hadamard inequality for strongly convex functions are proved. An useful characterization of strongly Schur convex functions F : I-n -> R by partial derivatives is given. As an application, a result on the strong Schur-concavity of the integral mean of the digamma function is obtained.