Multi-term refinements of real power inequalities for convex and log-convex functions

Abstract

We combine the idea of partitioning [0,1] into m equal subintervals, developed by Yang and Zhang [J. Math. Inequal. 19 (2025), 441–459], with weak submajorization techniques to derive a family of multi-term refinements of real power inequalities for convex and log-convex functions with double weights, which not only recover the earlier inequalities of Ighachane and Bouchangour [Oper. Matrices 17 , (2023), 213–233], but are also sharper than those obtained by Ighachane and Huy et al. [Rend. Circ. Mat. Palermo (2) 73 , (2024), 1101–1138] under certain parameter regimes. As applications, operator mean relations, as well as improved Heinz-type and Hölder-type matrix norm inequalities are given.