New versions of refinements and reverses of Young-type inequalities with the Kantorovich constant

Abstract

Recently, some Young-type inequalities have been promoted. The purpose of this article is to give further refinements and reverses to them with Kantorovich constants. Simultaneously, according to the scalar result, we have obtained some corresponding operator inequalities and matrix versions, including Hilbert-Schmidt norm, unitary invariant norm, and trace norm can be regarded as Scalar inequality.

Keywords

• young inequality
• kantorovich constant
• operator inequality
• operator means
• arithmetic-geometric-harmonic mean inequality
• 15a45
• 15a60