Some Combined Relations between Contractive Mappings, Kannan Mappings, Reasonable Expansive Mappings, and T-Stability

Abstract

In recent literature concerning fixed point theory for self-mappings T : X -> X in metric spaces (X,d), there are some new concepts which can be mutually related so that the inherent properties of each one might be combined for such self-mappings. Self-mappings T : X -> X can be referred to, for instance, as Kannan-mappings, reasonable expansive mappings, and Picard T-stable mappings. Some relations between such concepts subject either to sufficient, necessary, or necessary and sufficient conditions are obtained so that in certain self-mappings can exhibit combined properties being inherent to each of its various characterizations