Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
844840 | Nonlinear Analysis: Theory, Methods & Applications | 2006 | 11 Pages |
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)(P) of Lim and Xu.
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Authors
S. Dhompongsa, W.A. Kirk, Brailey Sims,