Schur convexity properties of the weighted arithmetic integral mean and Chebyshev functional. (English) Zbl 1299.26031
Summary: We discuss the Schur convexity, Schur geometrical convexity and Schur harmonic convexity of the weighted arithmetic integral mean and Chebyshev functional. Several sufficient conditions, and necessary and sufficient conditions are established.
MSC:
26B25 | Convexity of real functions of several variables, generalizations |
05E05 | Symmetric functions and generalizations |