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

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.
Full Text: DOI
[1] Bridson, M.; Haefliger, A., Metric spaces of nonpositive curvature, (1999), Springer-Verlag Berlin
[2] Kirk, W.A., Geodesic geometry and fixed point theory. II, (), 113-142 · Zbl 1083.53061
[3] Kirk, W.A., Geodesic geometry and fixed point theory, (), 195-225 · Zbl 1058.53061
[4] Aksoy, A.G.; Khamsi, M.A., A selection theorem in metric trees, Proc. amer. math. soc., 134, 2957-2966, (2006) · Zbl 1102.54022
[5] Kaewcharoen, A.; Kirk, W.A., Proximinality in geodesic spaces, Abstr. appl. anal., 2006, 1-10, (2006), Article ID 43591 · Zbl 1141.51011
[6] Kirk, W.A., Fixed point theorems in CAT(0) spaces and \(\mathbb{R}\)-trees, Fixed point theory appl., 4, 309-316, (2004) · Zbl 1089.54020
[7] Kirk, W.A.; Panyanak, B., A concept of convergence in geodesic spaces, Nonlinear anal., 68, 3689-3696, (2008) · Zbl 1145.54041
[8] Markin, J., Best approximation and fixed point theorems in hyperconvex metric spaces, Nonlinear anal., 63, 1841-1846, (2005)
[9] Dhompongsa, S.; Kaewkhao, A.; Panyanak, B., Lim’s theorem for multivalued mappings in CAT(0) spaces, J. math. anal. appl., 312, 478-487, (2005) · Zbl 1086.47019
[10] Shahzad, N.; Markin, J., Invariant approximation for commuting mappings in hyperconvex and CAT(0) spaces, J. math. anal. appl., 337, 1457-1464, (2008) · Zbl 1137.47043
[11] Kirk, W.A., Hyperconvexity of \(\mathbb{R}\)-trees, Fund. math., 156, 67-72, (1998) · Zbl 0913.54030
[12] Espinola, R.; Kirk, W.A., Fixed point theorems in \(\mathbb{R}\)-trees with applications to graph theory, Topology appl., 153, 1046-1055, (2006) · Zbl 1095.54012
[13] García-Falset, J.; Llorens-Fuster, E.; Prus, S., The fixed point property for mappings admitting a center, Nonlinear anal., 66, 1257-1274, (2007) · Zbl 1118.47043
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