Further inequalities involving the weighted geometric operator mean and the Heinz operator mean

Abstract

ABSTRACT In this paper, we first investigate some inequalities involving the p-weighted geometric operator mean where is a real number and A, B are two positive invertible operators acting on a Hilbert space. As applications, we obtain some inequalities about the so-called Tsallis relative operator entropy. We also give some inequalities involving the Heinz operator mean. Our results refine some inequalities existing in the literature. In a second part, we construct iterative algorithms converging to with a high rate of convergence. Some relationships involving are deduced. Numerical examples illustrating the theoretical results are also discussed.