Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces. (English) Zbl 1264.54068

Summary: Let \(X\) be a nonempty set and \(F:X\times X\rightarrow X\) be a given mapping. An element \((x,y)\in X\times X\) is said to be a coupled fixed point of the mapping \(F\) if \(F(x,y)=x\) and \(F(y,x)=y\). In this paper, we consider the case when \(X\) is a complete metric space endowed with a partial order. We define generalized Meir-Keeler type functions and we prove some coupled fixed point theorems under a generalized Meir-Keeler contractive condition. Some applications of our obtained results are given. The presented theorems extend and complement the recent fixed point theorems due to T. G. Bhaskar and V. Lakshmikantham [Nonlinear Anal., Theory Methods Appl. 65, No. 7, A, 1379–1393 (2006; Zbl 1106.47047)].


54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54E40 Special maps on metric spaces
54E50 Complete metric spaces


Zbl 1106.47047
Full Text: DOI


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