An improvement of Alzer-Fonseca-Kova\v cec's type inequalities with applications

Abstract

In this paper, we start by presenting multiple-term refinement of Young's and Young's type inequalities and its reverse using different weights, which extends and unifies two recent and important results due to M. Khosravi (Math. Slovaca \textbf{68} (2018), 803--810) and L. Nasiri et al. (Asian-European Journal Math. \textbf{15}, (2022) No. 07). Further, we mainly present some new real power inequalities of Young's inequality, extending a key results of Alzer et al. (Linear Multilinear Algebra \textbf{63}(3) (2015), 622--635), D. Q. Huy (Linear Algebra Appl. \textbf{656} (2023), 368--384) and J. Zhao (Bull. Malys. Math. Sci. Soc. \textbf{46}, No 52 (2023)).
As applications of these scalars results we obtain some inequalities for matrices, unitarily invariant norms and traces.