Summary: Two perturbation estimates of the maximal positive definite solutions to the matrix equations
are considered. These estimates are like to the estimates discussed by V. I. Hasanov
and I. G. Ivanov
[Linear Algebra Appl. 413, No. 1, 81–92 (2006; Zbl 1087.15016
)]. The conditions
in [loc. cit.] are not always satisfied. We replace this conditions by
is positive definite matrix. The theoretical results are illustrated by numerical examples.