Fixed points of uniformly lipschitzian mappings |
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Authors: | S Dhompongsa WA Kirk Brailey Sims |
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Institution: | 1. Department of Mathematics, Chiang Mai University, Chiang Mai, Thailand;2. Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USA;3. School of Mathematical and Physical Sciences, The University of Newcastle, NSW 2308, Australia |
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Abstract: | Two fixed point theorems for uniformly lipschitzian mappings in metric spaces, due respectively to E. Lifšic and to T.-C. Lim and H.-K. Xu, are compared within the framework of the so-called CAT(0) spaces. It is shown that both results apply in this setting, and that Lifšic’s theorem gives a sharper result. Also, a new property is introduced that yields a fixed point theorem for uniformly lipschitzian mappings in a class of hyperconvex spaces, a class which includes those possessing property (P) of Lim and Xu. |
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Keywords: | primary 54H25 54E40 secondary 47H09 |
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