Functions generating \((m,M,\Psi)\)-Schur-convex sums
This paper presents a new notion of $(m,M,\Psi)$- Schur-convex functions. The necessary and sufficient conditions for a function $f$ to generate $(m,M,\Psi)$-Schur-convex sums are derived, proved and discussed. By using this new concept, a counterpart of the classical Hardy-Littlewood-Polya majorization theorem was proved. Furthermore, a counterpart of the result of Ng stating that a function generates $(m,M,\Psi)$-Schur-convex sums if and only if it is $(m,M,\Psi)$-Wright-convex is proved and a characterization of $(m,M,\Psi)$-Wright-convex functions is given.
\((m, M, \psi)\)-convex (Jensen-convex, Wright-convex) functions
scientific article; zbMATH DE number 7035773
scientific article