On Delta-convergence theorems in CAT(0) spaces
By using the concept of Delta-convergence introduced by Lim [T.C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60 (1976) 179-182], we are able to give the CAT(0) space analogs of results on weak convergence of the Picard, Mann and Ishikawa iterates proved in uniformly convex Banach spaces by Opial [Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967) 591-597], Ishikawa [S. Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976) 65-71] and Tan and Xu [K.K. Tan, H.K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math, Anal. Appl. 178 (1993) 301-308]. (C) 2008 Elsevier Ltd. All rights reserved.
delta-convergence cat(0) spaces fixed points weak convergence nonexpansive mappings