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

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 A(f) (or type A(g)). These results generalize some known results.