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 68 (2018), 803-810) and L. Nasiri et al. (Asian-European Journal Math. 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 63(3) (2015), 622-635), D. Q. Huy et al. (Linear Algebra Appl. 656 (2023), 368-384) and J. Zhao (Bull. Malys. Math. Sci. Soc. 46, No 52 (2023)). As applications of these results, we provide some inequalities for matrices, unitarily invariant norms and traces.
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