(G, F)-closed set and coupled coincidence point theorems for a generalized compatible in partially metric spaces

Abstract

© 2016 by the Mathematical Association of Thailand. All rights reserved. In this work, we prove the existence of a coupled coincidence point theorem for a pair {F,G} of mapping F,G: X×X → X with ϕ- contraction map- pings in complete metric spaces without G-increasing property of F and mixed monotone property of G, using concept of (G, F)-closed set. We give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled coincidence point by G using the mixed monotone property. We also show the uniqueness of a coupled coincidence point of the given mapping. Further, we apply our results to the existence and uniqueness of a coupled coincidence point of the given mapping in partially ordered metric spaces.