Abstract
In this article, we study the existence of coupled coincidence points for multi-valued nonlinear contractions in partially ordered metric spaces. We do it from two different approaches, the first is Delta-symmetric property recently studied in Samet and Vetro (Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces, Nonlinear Anal. 74, 4260-4268 (2011)) and second one is mixed g-monotone property studied by Lakshmikantham and A dagger iriA double dagger (Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70, 4341-4349 (2009)).
The theorems presented extend certain results due to A dagger iriA double dagger (Multi-valued nonlinear contraction mappings, Nonlinear Anal. 71, 2716-2723 (2009)), Samet and Vetro (Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces, Nonlinear Anal. 74, 4260-4268 (2011)) and many others. We support the results by establishing an illustrative example.
2000 MSC: primary 06F30; 46B20; 47E10.