On the Weighted Chaotic Identric Mean of Two Accretive Matrices

Intensive studies aiming to extend the mean theory from scalar variables to matrix/operator arguments and to establish some properties for these matrix/operator extensions have been carried out recently. The contribution of this paper falls within this framework. We introduce the weighted chaotic identric mean of two accretive matrices. Among the obtained results, we present some inequalities about this weighted mean when the involved matrices are sector matrices. As an application, Heinz matrix mean and Heron matrix mean of chaotic types as well as another chaotic mean are derived and studied, as well.