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Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. (English) Zbl 1216.54021
Summary: We establish two coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. The theorems presented extend some results due to Lj. Ćirić [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7–8, A, 2716–2723 (2009; Zbl 1179.54053)]. An example is given to illustrate the usability of our results.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54C60 Set-valued maps in general topology
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