Coupled Fixed-Point Theorems for Contractions in Partially Ordered Metric Spaces and Applications

Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mapping F from X×X into X and a mapping g from X into X with some applications. The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and improve the recent fixed-point theorems due to Bessem Samet (2010). Indeed, we introduce the definition of generalized g-Meir-Keeler type contractions and prove some coupled fixed point theorems under a generalized g-Meir-Keeler-contractive condition. Also, some applications of the main results in this paper are given.