Operator iteration on the Young inequality

Abstract

Abstract In this paper, we employ iteration on operator version of the famous Young inequality and obtain more arithmetic-geometric mean inequalities and the reverse versions for positive operators. Concretely, we obtain refined Young inequalities with the Kantorovich constant, the reverse ratio type and difference type inequalities for arithmetic-geometric operator mean under different conditions.

Keywords

• operator iteration
• Young inequality
• arithmetic-geometric means
• Kantorovich constant