Coupled coincidence point results for probabilistic φ-contractions

Abstract

In this paper, we establish a new coupled coincidence point results in partially ordered probabilistic metric spaces by utilizing the Gauge function. We use the compatibility condition between two mappings. We use monotone and mixed monotone properties of functions with respect to the ordering. Our main result has several corollaries. The main result is supported with an example which shows that the corollaries are actually contained in our main theorem. The methodology is a combination of analytic and order theoretic approaches.