Have a personal or library account? Click to login
Convergence of Ishikawa type iteration process for three quasi-nonexpansive mappings in a convex metric space Cover

Convergence of Ishikawa type iteration process for three quasi-nonexpansive mappings in a convex metric space

Open Access
|Apr 2017

References

  1. [1] V. Berinde, Iterative Approximation of Fixed Points, Springer, Berlin Heidelberg New York, 200710.1109/SYNASC.2007.49
  2. [2] M. Bridson and A. Haeiger, Metric spaces of non-positive curvature, Springer-Verlag, Berlin, Heidelberg, New York, 1999.10.1007/978-3-662-12494-9
  3. [3] H. Busemann, Spaces with non-positive curvature, Acta Math. 80 (1948), 259-310.10.1007/BF02393651
  4. [4] Cegielski, A., Iterative methods for fixed point problems in Hilbert spaces, Lecture Notes in Mathematics, 2057, Springer, Heidelberg, 2012.10.1007/978-3-642-30901-4
  5. [5] Chidume, C. E., Geometric Properties of Banach Spaces and Nonlinear Iteration, Springer, Berlin Heidelberg New York, 2009.10.1007/978-1-84882-190-3
  6. [6] G. Das and P. Debata, Fixed points of quasi-nonexpansive mappings, Indian J. Pure Appl. Math. 17(1986), 1263-1269.
  7. [7] H. Fukhar-ud-din, A. R. Khan and Z. Akhtar, Fixed point results for a generalized nonexpansive map in uniformly convex metric spaces, Nonlin- ear Anal., 75 (2012), 4747-4760.10.1016/j.na.2012.03.025
  8. [8] M. K. Ghosh and L. Debnath, Convergence of Ishikawa iterates of quasi- nonexpansive mappings, J. Math. Anal. Appl., 207 (1997), 96-103.10.1006/jmaa.1997.5268
  9. [9] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150.10.1090/S0002-9939-1974-0336469-5
  10. [10] S. H. Khan and H. Fukhar-ud-din, Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Anal., 61 (2005), 1295 - 1301.10.1016/j.na.2005.01.081
  11. [11] A. R. Khan, H. Fukhar-ud-din and M. A. A. Khan, An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces, Fixed Point Theory and Applications, 2012, 2012:54 (doi:10.1186/1687-1812-2012-54).
  12. [12] A. R. Khan, H. Fukhar-ud-din and A.A. Domlo, Approximating fixed points of some maps in uniformly convex metric spaces, Fixed Point Theory Applications, 2010 (2010) Article ID 385986, 11 pages.10.1155/2010/385986
  13. [13] A. R. Khan, M. A. Khamsi and H. Fukhar-ud-din, Strong convergence of a general iteration scheme in CAT(0)-spaces, Nonlinear Anal. 74 (2011), 783-791.10.1016/j.na.2010.09.029
  14. [14] W. A. Kirk, An abstract fixed point theorem for nonexpansive mappings, Proc. Amer. Math. Soc., 82(1981), 640-642.10.1090/S0002-9939-1981-0614894-6
  15. [15] W. A. Kirk, Fixed point theory for nonexpansive mappings II, Contemporary Math.,18(1983), 121-140.10.1090/conm/018/728596
  16. [16] M. Maiti and M. K. Ghosh, Approximating fixed points by Ishikawa iterates, Bull. Austral. Math. Soc. 40 (1989), 113-I 17.10.1017/S0004972700003555
  17. [17] W. R. Mann, Mean value methods in iterations, Proc. Amer. Math. Soc. 4 (1953), 506-510.10.1090/S0002-9939-1953-0054846-3
  18. [18] J. P. Penot, Fixed point theorems without convexity, Bull. Soc. Math. France, 60(1979), 129-152.10.24033/msmf.266
  19. [19] T. Shimizu and W. Takahashi, Fixed points of multivalued mappings in certain convex metric spaces, Topol. Methods Nonlinear Anal. 8 (1996), 197-203.10.12775/TMNA.1996.028
  20. [20] W. Takahashi, A convexity in metric spaces and nonexpansive mappings, Kodai. Math. Sem. Rep., 22(1970), 142-149.10.2996/kmj/1138846111
DOI: https://doi.org/10.1515/auom-2015-0027 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 83 - 92
Submitted on: Jan 1, 2014
Accepted on: May 1, 2014
Published on: Apr 22, 2017
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2017 Hafiz Fukhar-ud-din, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.