Some result on Common Coupled Fixed Point Theorems for W-Compatible Mappings In Complex Valued Metric Spaces with an Applications

Bhashkar et al. [2] introduced the concept of coupled fixed point of mapping and investigated some coupled fixed point theorems in partially ordered sets. Lakshmikantham et al. [3] proved coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete metric spaces. In this paper we introduce the concept of w-compatible mappings to obtain coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in complex valued metric space.Coupled common fixed point theorems for such mappings are also proved. As an application of our main result, we prove some theorems for two finite families of mappings. Results are supported by some examples.