Some refinements of real power form inequalities for convex functions via weak sub-majorization

Abstract

. The main goal of this article, is to develop a general method for improving some new real power inequalities for convex and log-convex functions, which extends and uni fi es two recent and important results due to M. Sababheh [Linear Algebra Appl. 506 (2016), 588– 602] and D. Q. Huy et al. [Linear Algebra Appl. 656 (2023), 368–384]. Then by selecting some appropriate convex and log-convex functions, we obtain new mean inequalities for scalars and matrices, some new re fi nements and reverses of the Heinz and H¨older type inequalities for matrices. We get also some new and re fi ned trace and numerical radius inequalities. Mathematics