Further refinement of Young's type inequalities and its reversed using the Kantorovich constants

Abstract

In this paper, we show a multiple-term refinement of Young's type inequality and its reverse via the Kantorovich constants, which extends and unifies two recent and important results due to L. Nasiri et al. (Result. Math (74), 2019), and C. Yang et al. (Journal. Math. Inequalities, (14), 2020). An application of these scalars results we give a multiple-term refinement of Young's type inequalities for operators, Hilbert-Schmidt norms, Traces and the unitarily invariant norms.