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Lakshmikantham, V.; Ćirić, Ljubomir

Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. (English) Zbl 1176.54032

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 12, 4341-4349 (2009).
The authors introduce the concept of a g-monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces. The presented theorems are generalizations of 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)] and include several recent developments.
Reviewer: Yongxiang Li (Lanzhou)

Cited in 21 Reviews
Cited in 444 Documents

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
47H10 Fixed-point theorems
34B15 Nonlinear boundary value problems for ordinary differential equations

Keywords:

coupled fixed point; coupled coincidence; coupled common fixed point; partially ordered set; mixed monotone mapping

Citations:

Zbl 1106.47047
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\textit{V. Lakshmikantham} and \textit{L. Ćirić}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 12, 4341--4349 (2009; Zbl 1176.54032)
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References:

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