Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9502694 | Journal of Mathematical Analysis and Applications | 2005 | 10 Pages |
Abstract
Let X be a complete CAT(0) space. We prove that, if E is a nonempty bounded closed convex subset of X and T:EâK(X) a nonexpansive mapping satisfying the weakly inward condition, i.e., there exists pâE such that αpâ(1âα)TxâIE(x)¯âxâE, âαâ[0,1], then T has a fixed point. In Banach spaces, this is a result of Lim [On asymptotic centers and fixed points of nonexpansive mappings, Canad. J. Math. 32 (1980) 421-430]. The related result for unbounded R-trees is given.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
S. Dhompongsa, A. Kaewkhao, B. Panyanak,