Topological Methods in Nonlinear Analysis

Relaxed Halpern type iteration schemes for sequences of nonexpansive mappings in ${\rm CAT}(0)$ spaces

Wei-Qi Deng

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Abstract

Under weaker conditions on parameters, we prove strong convergence theorems of Halpern type iteration schemes for sequences of nonexpansive mappings in ${\rm CAT}(0)$ spaces. Since there is no assumption of the AKTT-condition imposed on the involved mappings, the results improve those of the authors with related researches.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 43, Number 1 (2014), 241-249.

Dates
First available in Project Euclid: 11 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1460381557

Mathematical Reviews number (MathSciNet)
MR3236444

Zentralblatt MATH identifier
1382.47019

Citation

Deng, Wei-Qi. Relaxed Halpern type iteration schemes for sequences of nonexpansive mappings in ${\rm CAT}(0)$ spaces. Topol. Methods Nonlinear Anal. 43 (2014), no. 1, 241--249. https://projecteuclid.org/euclid.tmna/1460381557


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References

  • M.R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, 319 , Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, Germany (1999) \ref\key 2
  • D. Burago, Y. Burago and S. Ivanov, A Course in Metric Geometry, 33 , Graduate Studies in Mathematics, Amer. Math. Soc., Providence, RI, USA (2001) \ref\key 3
  • P. Chaoha and A. Phon-on, A note on fixed point sets in \romCAT(0) spaces, J. Math. Anal. Appl., 320 , 983–987 (2006) \ref\key 4
  • S. Dhompongsa, W. Fupinwong and A. Kaewkhao, Common fixed points of a nonexpansive semigroup and a convergence theorem for Mann iterations in geodesic metric spaces , Nonlinear Anal., 70 , 4268–4273 (2009) \ref\key 5
  • S. Dhompongsa, A. Kaewkhao and B. Panyanak, Lim's theorems for multivalued mappings in \romCAT(0) spaces, J. Math. Anal. Appl., 312 , 478-487 (2005) \ref\key 6
  • S. Dhompongsa, W. A. Kirk and B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces , J. Nonlinear Convex Anal., 8 , 35–45 (2007) \ref\key 7
  • S. Dhompongsa, W. A. Kirk and B. Sims, Fixed points of uniformly Lipschitzian mappings , Nonlinear Anal., 65 , 762–772 (2006) \ref\key 8
  • S. Dhompongsa and B. Panyanak, On $\Delta$-convergence theorems in \romCAT(0) spaces, Comp. Math. Appl., 56 , 2572–2579 (2008) \ref\key 9
  • K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings, 83 , Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA (1984) \ref\key 10
  • N. Hussain and M.A. Khamsi, On asymptotic pointwise contractions in metric spaces , Nonlinear Anal., 71 , 4423–4429 (2009) \ref\key 11
  • A. Kaewcharoen and W.A. Kirk, Proximinality in geodesic spaces , Abstr. Appl. Anal., 2006 . Article ID 43591, 10 pages (2006) \ref\key 12
  • W.A. Kirk, Geodesic geometry and fixed point theory , Seminar of Mathematical Analysis (Malaga/Seville, 2002/2003), 64 , Colecc. Abierta, 195–225, Seville University Publications, Seville, Spain (2003) \ref\key 13 ––––, Geodesic geometry and fixed point theory \romII, International Conference on Fixed Point Theory and Applications, 113 –142, Yokohama Publications, Yokohama, Japan (2004) \ref\key 14 ––––, Fixed point theorems in \romCAT(0) spaces and $R$-trees, Fixed Point Theory Appl., 2004 , 309–316 (2004) \ref\key 15
  • L. Leustean, A quadratic rate of asymptotic regularity for \romCAT(0)-spaces, J. Math. Anal. Appl., 325 , 386–399 (2007) \ref\key 16
  • M.O. Osilike, S.C. Aniagbosor and B.G. Akuchu, Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces , Panamer. Math. J., 12 (2002), 77–88 \ref\key 17
  • S. Saejung, Halpern's iteration in \romCAT(0) spaces, Fixed Point Theory Appl., 2010 . Article ID 471781, 13 p. \ref\key 18
  • N. Shahzad, Fixed point results for multimaps in \romCAT(0) spaces, Topology Appl., 156 , 997–1001 (2009) \ref\key 19 ––––, Invariant approximations in \romCAT(0) spaces, Nonlinear Anal., 70 , 4338–4340 (2009) \ref\key 20
  • N. Shahzad and J. Markin, Invariant approximations for commuting mappings in \romCAT(0) and hyperconvex spaces, J. Math. Anal. Appl., 337 , 1457–1464 (2008)