2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139482We characterize real functions $f$ on an interval $(-α,α)$ for which the entrywise matrix function $[a_{ij}] \mapsto [f(a_{ij})]$ is positive, monotone and convex, respectively, in the positive semidefiniteness order. Fractional power functions are exemplified and related weak majorizations are shown.23 pages; Section 6 is considerably improvedFunctional Analysis15A45; 15A48text