Fixed Points of Nonexpansive Mappings in Banach Spaces

Volume 12, Issue 4, pp 295-303 http://dx.doi.org/10.22436/jmcs.012.04.05

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2107 Downloads
• 3225 Views

Authors

F. Golkar - Department of Mathematics, Shahid Chamran university of Ahvaz, Ahvaz, Iran. A. Dianatifar - Department of Mathematics, Shahid Chamran university of Ahvaz, Ahvaz, Iran. A. M. Aminpour - Department of Mathematics, Shahid Chamran university of Ahvaz, Ahvaz, Iran. M. Sadeghi - Department of Mathematics, Shahid Chamran university of Ahvaz, Ahvaz, Iran.

Abstract

In this paper we study the approximation of common fixed points of a finite family of nonexpansive mappings in uniformly smooth Banach spaces. Also we show that the convergence of the proposed algorithm can be proved under some types of control conditions.

Share and Cite

Keywords

• Nonexpansive mapping
• Strong convergence
• Common fixed point
• Uniformly smooth Banach space.

MSC

•  47H10
•  47H09

References

• [1] H. K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl., 659–678 (2000)
  • View Article
  • MathSciNet
  • Google Scholar


• [2] H. K. Xu , Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. , 298 (2004), 279-291.
  • View Article
  • Google Scholar


• [3] K. Goebel, S. Reich, Uniform Convexity, Nonexpansive mappings and Hyperbolic Geometry, Dekker (1984)
  • Google Scholar


• [4] S. Atsushiba, W. Takahashi , Strong convergence theorems for a finite family of nonexpansive mappings and applications, Indian J. Math. , 41 (1999), 435–453.
  • MathSciNet
  • Google Scholar


• [5] Sh. Banerjee, B. S. Choudhury, Weak and strong convergence theorems of a new iterative process with errors for common fixed points of a finite families of asymptotically nonexpansive mappings in the intermediate sense in Banach spaces, TJMCS, 11 (2014), 79-85.
  • Google Scholar


• [6] S. S. Chang, Some problems and results in the study of nonlinear analysis, Nonlinear Anal. , 33 (1997), 4197-4208.
  • View Article
  • MathSciNet
  • Google Scholar


• [7] T. Suzuki, Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals , J. Math. Anal. Appl., 305 (2005), 227-239.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] Y. Yao, A general iterative method for a finite family of nonexpansive mappings , Nonlinear Anal., 66 (2007), 2676-2687.
  • View Article
  • MathSciNet
  • Google Scholar