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Common coupled fixed point theorems in cone metric spaces for \(w\)-compatible mappings. (English) Zbl 1197.54049
Summary: We introduce the concept of \(w\)-compatible mappings to obtain coupled coincidence point and coupled point of coincidence theorems for nonlinear contractive mappings in cone metric spaces with a cone having nonempty interior. Coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend and unify several well-known comparable results in the literature. The results are supported by three examples.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
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