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Fixed points of periodic and firmly lipschitzian mappings in Banach spaces

Krzysztof Pupka — 2012

Commentationes Mathematicae Universitatis Carolinae

W.A. Kirk in 1971 showed that if T : C C , where C is a closed and convex subset of a Banach space, is n -periodic and uniformly k -lipschitzian mapping with k < k 0 ( n ) , then T has a fixed point. This result implies estimates of k 0 ( n ) for natural n 2 for the general class of k -lipschitzian mappings. In these cases, k 0 ( n ) are less than or equal to 2. Using very simple method we extend this and later results for a certain subclass of the family of k -lipschitzian mappings. In the paper we show that k 0 ( 3 ) > 2 in any Banach space. We also...

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