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On coincidence and common fixed points of nearly densifying mappings. (English) Zbl 0982.54032

Let \(A\) be a bounded subset of a metric space \((X,d)\) and \(\alpha(A)\) be the Kuratowski measure of noncompactness of \(A\). A mapping \(f: X\to X\) is said to be nearly densifying if \(\alpha(f(A))<\alpha(A)\) for every bounded and \(f\)-invariant subset \(A\) of \(X\) with \(\alpha(A)> 0\).
In the present paper the authors establish some coincidence and common fixed point theorems for certain nearly densifying mappings in complete metric spaces. These results unify a lot of previously known theorems.

MSC:

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