Schur-convexity of averages of convex functions (Q535531)

The properties of Schur-convexity and Schur-concavity have invoked the interest of many researchers, and numerous papers have been dedicated to the investigation of them. The authors' object is to present 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 quasi-arithmetic mean is studied. Relations to some already published results are established, and some applications of the extended results are produced. 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. This paper contains lots of interesting interrelations with Schur-convexity.