On Δ-convergence theorems in CAT(0) spaces

Authors:
S. Dhompongsa;B. Panyanak
Affiliations:
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand;Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 1
Cited 2

Nonexpansive iterations in hyperbolic spaces

Nonlinear Analysis: Theory, Methods & Applications

Strong and Δ-convergence of some iterative schemes in CAT(0) spaces

Computers & Mathematics with Applications
Fixed point and convergence theorems for different classes of generalized nonexpansive mappings in CAT(0) spaces

Computers & Mathematics with Applications

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Abstract

By using the concept of @?-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].