Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2013), Article ID 821737, 7 pages.

Approximation Analysis for a Common Fixed Point of Finite Family of Mappings Which Are Asymptotically k -Strict Pseudocontractive in the Intermediate Sense

H. Zegeye and N. Shahzad

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Abstract

We introduce an iterative process which converges strongly to a common fixed point of a finite family of uniformly continuous asymptotically k i -strict pseudocontractive mappings in the intermediate sense for i = 1 , 2 , , N . The projection of x 0 onto the intersection of closed convex sets C n and Q n for each n 1 is not required. Moreover, the restriction that the interior of common fixed points is nonempty is not required. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 821737, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807687

Digital Object Identifier
doi:10.1155/2013/821737

Mathematical Reviews number (MathSciNet)
MR3064879

Zentralblatt MATH identifier
1266.47100

Citation

Zegeye, H.; Shahzad, N. Approximation Analysis for a Common Fixed Point of Finite Family of Mappings Which Are Asymptotically $k$ -Strict Pseudocontractive in the Intermediate Sense. J. Appl. Math. 2013, Special Issue (2013), Article ID 821737, 7 pages. doi:10.1155/2013/821737. https://projecteuclid.org/euclid.jam/1394807687


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References

  • Q. H. Liu, “Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemi-contractive mappings,” Nonlinear Analysis, vol. 26, pp. 1838–1842, 1996.
  • Y. X. Tian, S.-S. Chang, J. Huang, X. Wang, and J. K. Kim, “Implicit iteration process for common fixed points of strictly asymptotically pseudocontractive mappings in Banach spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 324575, 12 pages, 2008.
  • T.-H. Kim and H.-K. Xu, “Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions,” Nonlinear Analysis, vol. 68, no. 9, pp. 2828–2836, 2008.
  • D. R. Sahu, H.-K. Xu, and J.-C. Yao, “Asymptotically strict pseudocontractive mappings in the intermediate sense,” Nonlinear Analysis, vol. 70, no. 10, pp. 3502–3511, 2009.
  • C. S. Hu and G. Cai, “Convergence theorems for equilibrium problems and fixed point problems of a finite family of asymptotically $k$-strictly pseudocontractive mappings in the intermediate sense,” Computers & Mathematics with Applications, vol. 61, no. 1, pp. 79–93, 2011.
  • H. Zegeye, M. Robdera, and B. Choudhary, “Convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense,” Computers & Mathematics with Applications, vol. 62, no. 1, pp. 326–332, 2011.
  • H. Zegeye and N. Shahzad, “Convergence of Manns type iteration method for generalized asymptotically nonexpansive mappings,” Computers and Mathematics With Applications, vol. 62, no. 11, pp. 4007–4014, 2011.
  • P.-E. Maingé, “Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization,” Set-Valued Analysis, vol. 16, no. 7-8, pp. 899–912, 2008.
  • J. G. O'Hara, P. Pillay, and H.-K. Xu, “Iterative approaches to convex feasibility problems in Banach spaces,” Nonlinear Analysis, vol. 64, no. 9, pp. 2022–2042, 2006.
  • W. Takahashi, Nonlinear Functional Analysis-Fixed Point Theory and Applications, Yokohama Publishers, Yokohama, Japan, 2000.
  • T.-H. Kim and H.-K. Xu, “Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups,” Nonlinear Analysis, vol. 64, no. 5, pp. 1140–1152, 2006.