Abstract and Applied Analysis

Strong Convergence Theorems for Solutions of Equilibrium Problems and Common Fixed Points of a Finite Family of Asymptotically Nonextensive Nonself Mappings

Lijuan Zhang, Hui Tong, and Ying Liu

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Abstract

An iterative algorithm for finding a common element of the set of common fixed points of a finite family of asymptotically nonextensive nonself mappings and the set of solutions for equilibrium problems is discussed. A strong convergence theorem of common element is established in a uniformly smooth and uniformly convex Banach space.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 494632, 6 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607605

Digital Object Identifier
doi:10.1155/2014/494632

Mathematical Reviews number (MathSciNet)
MR3206794

Zentralblatt MATH identifier
07022484

Citation

Zhang, Lijuan; Tong, Hui; Liu, Ying. Strong Convergence Theorems for Solutions of Equilibrium Problems and Common Fixed Points of a Finite Family of Asymptotically Nonextensive Nonself Mappings. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 494632, 6 pages. doi:10.1155/2014/494632. https://projecteuclid.org/euclid.aaa/1412607605


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References

  • A. Moudafi, “Weak convergence theorems for nonexpansive mappings and equilibrium problems,” Journal of Nonlinear and Convex Analysis, vol. 9, no. 1, pp. 37–43, 2008.
  • A. Tada and W. Takahashi, “Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem,” Journal of Optimization Theory and Applications, vol. 133, no. 3, pp. 359–370, 2007.
  • L.-C. Ceng and J.-C. Yao, “A hybrid iterative scheme for mixed equilibrium problems and fixed point problems,” Journal of Computational and Applied Mathematics, vol. 214, no. 1, pp. 186–201, 2008.
  • S. Takahashi and W. Takahashi, “Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 331, no. 1, pp. 506–515, 2007.
  • P. L. Combettes and S. A. Hirstoaga, “Equilibrium programming in Hilbert spaces,” Journal of Nonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, 2005.
  • Y. I. Alber, “Metric and generalized projection operators in Banach spaces: properties and applications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, vol. 178, pp. 15–50, Marcel Dekker, New York, NY, USA, 1996.
  • C. E. Chidume, M. Khumalo, and H. Zegeye, “Generalized projection and approximation of fixed points of nonself maps,” Journal of Approximation Theory, vol. 120, no. 2, pp. 242–252, 2003.
  • Y. Liu, “Convergence theorems for common fixed points of nonself asymptotically nonextensive mappings,” Journal of Optimization Theory and Applications, 2013.
  • L. Yang and X. Xie, “Weak and strong convergence theorems of three step iteration process with errors for nonself-asymptotically nonexpansive mappings,” Mathematical and Computer Modelling, vol. 52, no. 5-6, pp. 772–780, 2010.
  • S.-y. Matsushita and W. Takahashi, “A strong convergence theorem for relatively nonexpansive mappings in a Banach space,” Journal of Approximation Theory, vol. 134, no. 2, pp. 257–266, 2005.
  • H. K. Xu, “Inequalities in Banach spaces with applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 16, no. 12, pp. 1127–1138, 1991.
  • E. Blum and W. Oettli, “From optimization and variational inequalities to equilibrium problems,” The Mathematics Student, vol. 63, no. 1–4, pp. 123–145, 1994. \endinput