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Fixed points of weak contractions in cone metric spaces. (English) Zbl 1191.54036

In the paper weak contractions in cone metric spaces (generalization of a metric space) are considered. It is proved that such a mapping has a unique fixed point given as the limit of a sequence of consecutive approximations.
The proof of this result utilizes the ideas of the proof of the well known Banach fixed point theorem for strict contractions in complete metric spaces.
The example presented in the paper is not very interesting because the fixed point of this transformation is obvious.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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