109
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Viscosity Iteration in CAT(κ) Spaces

Pages 1245-1264 | Received 20 Jul 2012, Accepted 14 Jan 2013, Published online: 25 Sep 2013

REFERENCES

  • I. Berg and I. Nikolaev ( 1998 ). On a distance between directions in an Alexandrov space of curvature ≤K . Michigan Math. J. 45 : 257 – 289 .
  • M. Bridson and A. Haefliger ( 1999 ). Metric Spaces of non-Positive Curvature . Springer-Verlag , Berlin .
  • D. Burago , Y. Burago , and S. Ivanov ( 2001 ). A Course in Metric Geometry . Graduate Studies in Mathematics, Vol. 33. American Mathematical Society, Providence, RI .
  • C. E. Chidume and C. O. Chidume ( 2006 ). Iterative approximation of fixed points of nonexpansive mappings . J. Math. Anal. Appl. 318 : 288 – 295 .
  • L. Y. Shi and R. D. Chen ( 2012 ). Strong nonvergence of viscosity approximation methods for nonexpansive mappings in CAT(0) spaces . J. Appl. Math.
  • S. Dhompongsa and B. Panyanak ( 2008 ). On Δ–convergence theorems in CAT(0) spaces . Comput. Math. Appl. 56 : 2572 – 2579 .
  • R. Espínola and A. Fernández-León ( 2009 ). CAT(κ)-spaces, weak convergence and fixed points . J. Math. Anal. Appl. 353 : 410 – 427 .
  • R. Espínola , A. Fernández-León , and B. Pia¸tek ( 2010 ). Fixed points of single- and set-valued mappings in uniformly convex metric spaces with no metric monvexity . Fixed Point Theory Appl.
  • K. Goebel and W. A. Kirk ( 1990 ). Topics in Metric Fixed Point Theory . Cambridge University Press , Cambridge , UK .
  • K. Goebel and S. Reich ( 1984 ). Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings . Pure and Applied Mathematics. Marcel Dekker , New York .
  • J. S. He , D. H. Fang , G. López , and C. Li ( 2011 ). Mann's algorithm for nonexpansive mappings in CAT(κ) spaces . Nonlinear Anal. 75 : 445 – 452 .
  • S. H. Khan and M. Abbas ( 2011 ). Strong and Δ–convergence of some iterative schemes in CAT(0) spaces . Comput. Math. Appl. 61 : 109 – 116 .
  • A. R. Khan , M. A. Khamsi , and H. Fukhar-ud-din ( 2011 ). Strong convergence of a general iteration scheme in CAT(0) spaces . Nonlinear Anal. 74 : 783 – 791 .
  • W. A. Kirk and B. Panyanak ( 2008 ). A concept of convergence in geodesic spaces . Nonlinear Anal. 68 : 3689 – 3696 .
  • W. A. Kirk and B. Sims (Eds.) ( 2001 ). Handbook of Metric Fixed Point Theory . Kluwer Academic Publishers .
  • E. Kopecká and S. Reich ( 2008 ). A note on the approximation of fixed points in the Hilbert ball . J. Nonlinear Convex Anal. 9 : 361 – 367 .
  • W. Laowang and B. Panyanak ( 2010 ). Approximating fixed points of nonexpansive nonself mappings in CAT(0) spaces . Fixed Point Theory Appl. p. 11 .
  • A. Moudafi ( 2000 ). Viscosity approximation methods for fixed–points problems . J. Math. Anal. Appl. 241 : 46 – 55 .
  • W. Nilsrakoo and S. Saejung (2010). Equilibrium problems and Moudafi's viscosity approximation methods in Hilbert spaces. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 17:195–213.
  • B. Pia¸tek ( 2011 ). Halpern iterations in CAT(κ) spaces . Acta Math. Sinica (English Ser.) 27 : 635 – 646 .
  • S. Saejung ( 2010 ). Halpern's iteration in CAT(0) spaces . Fixed Point Theory Appl .
  • T. Suzuki ( 2005 ). Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces . Fixed Point Theory Appl. XX : 103 – 123 .
  • H.-K. Xu ( 2002 ). Iterative algorithms for nonlinear operators . J. London Math. Soc. 66 : 240 – 256 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.