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

Abstract

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.