Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 658905, 11 pages.

Two General Algorithms for Computing Fixed Points of Nonexpansive Mappings in Banach Spaces

Shuang Wang

Full-text: Open access

Abstract

Recently, Yao et al. (2011) introduced two algorithms for solving a system of nonlinear variational inequalities. In this paper, we consider two general algorithms and obtain the extension results for computing fixed points of nonexpansive mappings in Banach spaces. Moreover, the fixed points solve the same system of nonlinear variational inequalities.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 658905, 11 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357180278

Digital Object Identifier
doi:10.1155/2012/658905

Mathematical Reviews number (MathSciNet)
MR2923344

Zentralblatt MATH identifier
1366.47032

Citation

Wang, Shuang. Two General Algorithms for Computing Fixed Points of Nonexpansive Mappings in Banach Spaces. J. Appl. Math. 2012, Special Issue (2012), Article ID 658905, 11 pages. doi:10.1155/2012/658905. https://projecteuclid.org/euclid.jam/1357180278


Export citation

References

  • Y. Yao, Y.-C. Liou, S. M. Kang, and Y. Yu, “Algorithms with strong convergence for a system of nonlinear variational inequalities in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 74, no. 17, pp. 6024–6034, 2011.
  • S. Wang and C. Hu, “Two new iterative methods for a countable family of nonexpansive mappings in Hilbert spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 852030, 12 pages, 2010.
  • Y. Yao, Y. C. Liou, and G. Marino, “Strong convergence of two iterative algorithms for nonexpansive mappings in Hilbert spaces,” Fixed Point Theory and Applications, vol. 2009, Article ID 279058, 7 pages, 2009.
  • Y. J. Cho, Y. Yao, and H. Zhou, “Strong convergence of an iterative algorithm for accretive operators in Banach spaces,” Journal of Computational Analysis and Applications, vol. 10, no. 1, pp. 113–125, 2008.
  • Y. Yao, Y.-C. Liou, and S. M. Kang, “Two-step projection čommentComment on ref. [11?]: Please update the information of this reference [11?], if possible.methods for a system of variational inequality problems in Banach spaces,” Journal of Global Optimization. In press.
  • H. K. Xu, “Inequalities in Banach spaces with applications,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 16, no. 12, pp. 1127–1138, 1991.
  • S. Reich, “Weak convergence theorems for nonexpansive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 67, no. 2, pp. 274–276, 1979.
  • K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, vol. 28 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1990.
  • L. S. Liu, “Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 194, no. 1, pp. 114–125, 1995.
  • H.-K. Xu, “Iterative algorithms for nonlinear operators,” Journal of the London Mathematical Society. Second Series, vol. 66, no. 1, pp. 240–256, 2002.
  • T. Suzuki, “Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals,” Journal of Mathematical Analysis and Applications, vol. 305, no. 1, pp. 227–239, 2005.