  We establish a reverse inequality for Tsallis relative operator entropy
involving a positive linear map. In addition, we present converse of Ando's
inequality, for each parameter. We give examples to compare our results with
the known results by Furuta and Seo. In particular, we establish an extension
and a reverse of the L\"owner-Heinz inequality under certain condition. Some
interesting consequences of inner product spaces and norm inequalities are also
presented.
