  The main purpose of this article is to study estimates for the Tsallis
relative operator entropy, by the use of Hermite-Hadamard inequality. Thus, we
obtain alternative bounds for the Tsallis relative operator entropy. In the
process to derive these bounds, we established the significant relation between
the Tsallis relative operator entropy and the generalized relative operator
entropy. In addition, we study the properties on monotonicity for the weight of
operator means, and for the parameter of relative operator entropies.
