New progress on the operator inequalities involving improved Young’s and its reverse inequalities relating to the Kantorovich constant

Abstract

Abstract The purpose of this paper is to give a survey of the progress, advantages and limitations of various operator inequalities involving improved Young’s and its reverse inequalities related to the Kittaneh-Manasrah inequality. We also present our new progress to the related research topics. New scalar versions of Young’s inequalities are promoted, the operator version and the Hilbert-Schmidt form also get a promotion.

Keywords

• Young’s inequality
• Kittaneh-Manasrah inequality
• Kantorovich constant
• operator inequality
• progress