Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces

Abstract

In this paper we introduce generalized symmetric Meir-Keeler contractions and prove some coupled fixed point theorems for mixed monotone operators F : X × X → X in partially ordered metric spaces. The obtained results extend, complement and unify some recent coupled fixed point theorems due to Samet (Nonlinear Anal. 72:4508-4517, 2010), Bhaskar and Lakshmikantham (Nonlinear Anal. 65:1379-1393, 2006) and some other very recent papers. An example to show that our generalizations are effective is also presented. © 2012 Berinde and Pǎcurar; licensee Springer.