In a series of recent papers (\cite{HT},\cite{HL},\cite{HL2},\cite{HLB}), Husain and Latif et al defined the notions of contractive-type and of nonexpansive-type multivalued
mappings and presented theorems that are designed to  generalize  the well known theorems concerning the fixed points of nonexpansive and contractive
multivalued
mappings. In this note, we present some results that generalize theorem 2.3 of \cite{HL2}. We also point out in this note that most of the theorems in the aforementioned papers, in light of conditions under which they were presented, do not generalize the existing theorems of nonexpansive mappings.  Some remarks on Definition 2.1 made by Husain and Tarafdar in \cite{HT} are also included.