No abstract

We extend the notion of R-weak commutativity and its variants to probabilistic metric spaces and prove common xed point theorems concerning them. Examples are included to reect upon the distinctiveness of the types of mappings dened in the paper.

We extend the recent results of coupled coincidence point theorems of by weakening the concept of mixed g-monotone property. We also give an example of a nonlinear contraction mapping, which is not applied to the existence of coupled coincidence point by the results of Shatanawi et. al. but can be applied to our results. The main results extend and unify the results of Shatanawi et. al. and many results of the coupled fixed point theorems of Sintunavarat et. al. (2012).

In this article, we introduce a new type of contraction and prove a coincidence point theorem which generalizes some known results in this area. The artile includes examples which show the validity of our result and that these contractions form a superclass of many classes of contractions known in the litrature.