Coupled coincidence point theorems for a α-ψ-contractive mapping in partially metric spaces with M-invariant set

Abstract

© 2015 by the Mathematical Association of Thailand. All rights reserved. In this paper, we introduce the notion M-invariant set for mapping α : X2× X2→ [0,+∞). We showed the existence of a coupled coincidence point theorem for a α-ψ-contractive mapping in partially ordered complete metric spaces without the mixed g-monotone property, using the concept of M-invariant set. We also show the uniqueness of a coupled common fixed point for such mappings and give some examples to show the validity of our result.