Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces
1 Department of Mathematics and Computer Science, North University of Baia Mare, Victoriei 76, Baia Mare, 430122, Romania
2 Department of Statistics, Analysis, Forecast and Mathematics, Faculty of Economics and Bussiness Administration, Babeş-Bolyai University of Cluj-Napoca, 56-60 T. Mihali St., Cluj-Napoca, 400591, Romania
Fixed Point Theory and Applications 2012, 2012:115 doi:10.1186/1687-1812-2012-115Published: 20 July 2012
In this paper we introduce generalized symmetric Meir-Keeler contractions and prove some coupled fixed point theorems for mixed monotone operators 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.