Invariant approximations in CAT(0) spaces. (English) Zbl 1167.47042

Shahzad, Naseer

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 12, 4338-4340 (2009).

Summary: Some common fixed point and invariant approximation results for CAT(0) spaces are obtained. Our results improve and extend some results of N. Shahzad and J. Markin [J. Math. Anal. Appl. 337, No. 2, 1457–1464 (2008; Zbl 1137.47043)] and of S. Dhompongsa, A. Kaewkhao and B. Panyanak [J. Math. Anal. Appl. 312, No. 2, 478–487 (2005; Zbl 1086.47019)].

MSC:

47H10	Fixed-point theorems
41A65	Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
54H25	Fixed-point and coincidence theorems (topological aspects)
58C30	Fixed-point theorems on manifolds
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

invariant approximation; nonexpansive mapping; CAT(0) space

References:

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