Coupled fixed point theorems for a generalized Meir–Keeler contraction in partially ordered metric spaces

Let X be a non-empty set and F : X × X → X be a given mapping. An element ( x , y ) ∈ X × 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 gene...

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Veröffentlicht in:Nonlinear analysis 2010-06, Vol.72 (12), p.4508-4517
1. Verfasser: Samet, Bessem
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Sprache:eng
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Zusammenfassung:Let X be a non-empty set and F : X × X → X be a given mapping. An element ( x , y ) ∈ X × 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 Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379–1393].
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2010.02.026