Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces

Abstract

The purpose of this paper is to prove that orbital continuity for a pair of self-mappings is a necessary and sufficient condition for the existence and uniqueness of a common fixed point for these mappings defined on Menger PM-spaces with a nonlinear contractive condition. The main results are obtained using the notion of R-weakly commutativity of type Af (or type Ag). These results generalize some known results.

Keywords

• probabilistic metric spaces
• common fixed point
• <i>R</i>-weakly commuting mappings
• nonlinear contractive condition