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Compatible and weakly compatible mappings in cone metric spaces. (English) Zbl 1205.54041

Summary: We extend and generalize common fixed point theorems for six self-maps of B.Singh and S.Jain [J. Math.Anal.Appl.301, No.2, 439–448 (2005; Zbl 1068.54044)] from Menger and metric spaces to cone metric spaces. We also extend the notions of compatible and weakly compatible mappings from the setting of Menger and metric spaces to the setting of cone metric spaces. We do not impose the normality property on the cone, but suppose only that the cone \(P\), in the ordered Banach space \(E\), has a nonempty interior. Examples are given to illustrate the results.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)

Citations:

Zbl 1068.54044
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References:

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