( G , F ) -Closed set and tripled point of coincidence theorems for generalized compatibility in partially metric spaces

Abstract

In this work, we prove the existence of a tripled point of coincidence theorem for a pair {F, G} of mappings F, G : X × X × X → X with ϕ-contraction mappings in partially ordered metric spaces without G-increasing property of F and mixed monotone property of G, using the concept of a (G, F)-closed set. We give some examples of a nonlinear contraction mapping, which is not applied to the existence of tripled coincidence point by G using the mixed monotone property. We also show the uniqueness of a tripled point of coincidence of the given mapping. Further, we apply our results to the existence and uniqueness of a tripled point of coincidence of the given mapping with G-increasing property of F and mixed monotone property of G in partially ordered metric spaces.