Schur-Convexity of Averages of Convex Functions

The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First, Schur-convexity of the generalized integral and weighted integral quasiarithmetic mean is studied. Relation to some already published results is established, and some applications of the extended result are given. Furthermore, Schur-convexity of functions connected to the Hermite-Hadamard inequality is investigated. Finally, some results on convexity and Schur-convexity involving divided difference are considered.