Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces

Suppose that is a nonempty closed convex subset of a complete CAT(0) space with the nearest point projection from onto . Let be a nonexpansive nonself mapping with . Suppose that is generated iteratively by , , , where and are real sequences in for some . Then -converges to some point in . This is an analog of a result in Banach spaces of Shahzad (2005) and extends a result of Dhompongsa and Panyanak (2008) to the case of nonself mappings.

[1]  Jacques Tits,et al.  Groupes Réductifs Sur Un Corps Local , 1972 .

[2]  Sompong Dhompongsa,et al.  Common fixed points of a nonexpansive semigroup and a convergence theorem for Mann iterations in geodesic metric spaces , 2009 .

[3]  A. Phon-on,et al.  A note on fixed point sets in CAT(0) spaces , 2006 .

[4]  D. Burago,et al.  A Course in Metric Geometry , 2001 .

[5]  S. Stević.  APPROXIMATING FIXED POINTS OF NONEXPANSIVE MAPPINGS , 2006 .

[6]  Naseer Shahzad,et al.  Invariant approximations for commuting mappings in CAT(0) and hyperconvex spaces , 2008 .

[7]  D. R. Smart.  Fixed Point Theorems , 1974 .

[8]  M. Gromov.  Metric Structures for Riemannian and Non-Riemannian Spaces , 1999 .

[9]  M. Bridson,et al.  Metric Spaces of Non-Positive Curvature , 1999 .

[10]  J. Schu,et al.  Weak and strong convergence to fixed points of asymptotically nonexpansive mappings , 1991, Bulletin of the Australian Mathematical Society.

[11]  William A. Kirk,et al.  FIXED POINT THEOREMS IN CAT(0) SPACES AND R-TREES , 2009 .

[12]  William A. Kirk,et al.  A concept of convergence in geodesic spaces , 2008 .

[13]  William A. Kirk,et al.  Fixed point theorems in spaces and -trees , 2004 .

[14]  William A. Kirk,et al.  Fixed points of uniformly lipschitzian mappings , 2006 .

[15]  N. Shahzad.  Fixed point results for multimaps in CAT(0) spaces , 2009 .

[16]  Laurentiu Leustean.  A quadratic rate of asymptotic regularity for CAT(0)-spaces , 2005 .

[17]  S. Dhompongsa,et al.  On -convergence theorems in CAT(0) spaces , 2008, Comput. Math. Appl..

[18]  Naseer Shahzad.  Invariant approximations in CAT(0) spaces , 2009 .

[19]  Naseer Shahzad,et al.  Approximating fixed points of non-self nonexpansive mappings in Banach spaces , 2005 .

[20]  Sompong Dhompongsa,et al.  Lim's theorems for multivalued mappings in CAT(0) spaces☆ , 2005 .

[21]  S. Reich,et al.  Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings , 1984 .

[22]  William A. Kirk,et al.  PROXIMINALITY IN GEODESIC SPACES , 2006 .

[23]  M. S. Khan.  REMARKS ON SOME FIXED POINT THEOREMS , 1982 .

[24]  Nawab Hussain,et al.  On asymptotic pointwise contractions in metric spaces , 2009 .

[25]  M. Birkner,et al.  Blow-up of semilinear PDE's at the critical dimension. A probabilistic approach , 2002 .