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Zbl 1145.54041
Kirk, W.A.; Panyanak, B.
A concept of convergence in geodesic spaces.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 68, No. 12, A, 3689-3696 (2008). ISSN 0362-546X

In the present paper, a {\it CAT(0) space} is a geodesic space for which each geodesic triangle is at least as `thin' as its comparison triangle in the Euclidean plane. A notion of convergence introduced independently by {\it T.-C. Lim} [Proc. Am. Math. Soc. 60, 179--182 (1976; Zbl 0346.47046)] and {\it T. Kuczumow} [Ann. Univ. Mariae Curie-Skłodowska, Sect. A 32, 79--88 (1978; Zbl 0463.47035)] is shown in CAT(0) spaces to be very similar to the usual weak convergence in Banach spaces. In particular, many Banach space results involving weak convergence have precise analogues in this setting. The paper ends with several open questions.
[In-Sook Kim (München)]
MSC 2000:
*54H25 Fixed-point theorems in topological spaces
54E40 Special maps on metric spaces
05C05 Trees

Keywords: CAT(0) space; $\varDelta$-convergence; weak convergence; fixed point

Citations: Zbl 0346.47046; Zbl 0463.47035

Cited in: Zbl 1182.47043

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