ABSTRACT
In this paper, we first investigate some inequalities involving the p-weighted geometric operator mean
where p ∈ [0, 1] 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.
Acknowledgments
The authors would like to express their sincere thanks to the two anonymous referees for their valuable comments and suggestions which allowed us to correct some mistakes and errors from the old version of the manuscript. Their useful remarks have substantially helped improve the quality of the final version of the present paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).