Strong Schur-Convexity of the Integral Mean

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.