Further refinements of Young’s type inequality for positive linear maps

Abstract

In this work, we give a multiple-term refinement of Young’s inequality which allow us to generalize and unify several results. As applications, we provide further refinements of a reversed AM–GM operator inequalities which extends and unifies two recent and important results due to Yang et al. (Math Slovaca 69:919–930, 2019) and Ren et al. (J Inequal Appl 2020:98, 2020) for positive linear maps and matrices. Also, our work deals with several other related results to both scalar and operator versions of the generalized Young’s inequality. In particular, we give a multiple-term refinement of Young’s inequalities for Hilbert–Schmidt norm, the determinants and the traces of positive definite matrices.