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Remarks on Lipschitzian mappings and some fixed point theorems. (English) Zbl 1146.47034

Let \(X\) and \(Y\) be normed spaces, \(C\) be a convex subset of \(X\) and let \(T: C\to Y\) be a continuous mapping. Then, under some additional conditions about \(T\), some results saying that \(T\) is a Lipschitzian mapping are presented.
These results are applied to a mapping defined on a subset of a uniformly convex Banach space to get some fixed point theorems.

MSC:

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