Abstract and Applied Analysis

A New Iterative Scheme of Modified Mann Iteration in Banach Space

Jinzuo Chen, Dingping Wu, and Caifen Zhang

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Abstract

We introduce the modified iterations of Mann's type for nonexpansive mappings and asymptotically nonexpansive mappings to have the strong convergence in a uniformly convex Banach space. We study approximation of common fixed point of asymptotically nonexpansive mappings in Banach space by using a new iterative scheme. Applications to the accretive operators are also included.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 264909, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273156

Digital Object Identifier
doi:10.1155/2014/264909

Mathematical Reviews number (MathSciNet)
MR3170395

Zentralblatt MATH identifier
07022047

Citation

Chen, Jinzuo; Wu, Dingping; Zhang, Caifen. A New Iterative Scheme of Modified Mann Iteration in Banach Space. Abstr. Appl. Anal. 2014 (2014), Article ID 264909, 9 pages. doi:10.1155/2014/264909. https://projecteuclid.org/euclid.aaa/1412273156


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References

  • F. E. Browder, “Fixed-point theorems for noncompact mappings in Hilbert space,” Proceedings of the National Academy of Sciences of the United States of America, vol. 53, pp. 1272–1276, 1965.
  • K. Goebel and W. A. Kirk, “A fixed point theorem for asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 35, pp. 171–174, 1972.
  • W. R. Mann, “Mean value methods in iteration,” Proceedings of the American Mathematical Society, vol. 4, pp. 506–510, 1953.
  • F. E. Browder and W. V. Petryshyn, “Construction of fixed points of nonlinear mappings in Hilbert space,” Journal of Mathematical Analysis and Applications, vol. 20, pp. 197–228, 1967.
  • C. Byrne, “A unified treatment of some iterative algorithms in signal processing and image reconstruction,” Inverse Problems, vol. 20, no. 1, pp. 103–120, 2004.
  • B. Halpern, “Fixed points of nonexpanding maps,” Bulletin of the American Mathematical Society, vol. 73, pp. 957–961, 1967.
  • T.-H. Kim and H.-K. Xu, “Strong convergence of modified Mann iterations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 61, no. 1-2, pp. 51–60, 2005.
  • K. Nammanee, M. A. Noor, and S. Suantai, “Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 314, no. 1, pp. 320–334, 2006.
  • 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.
  • H. F. Senter and W. G. Dotson, Jr., “Approximating fixed points of nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 44, pp. 375–380, 1974.
  • H.-K. Xu, “Iterative algorithms for nonlinear operators,” Journal of the London Mathematical Society, vol. 66, no. 1, pp. 240–256, 2002.
  • J. Schu, “Weak and strong convergence to fixed points of asymptotically nonexpansive mappings,” Bulletin of the Australian Mathematical Society, vol. 43, pp. 153–159, 1991.
  • Y. J. Cho, H. Y. Zhou, and G. T. Guo, “Weak and strong con-vergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings,” Computers & Mathematics with Applications, vol. 47, no. 4-5, pp. 707–717, 2004.
  • K. S. Kim, “Approximating common fixed points of nonspread-ing-type mappings and nonexpansive mappings in a Hilbert space,” Abstract and Applied Analysis, vol. 2012, Article ID 594218, 18 pages, 2012.
  • V. Barbu, Nonlinear Semi-Groups and Differential Equations in Banach Space, Noordhoff, Leiden, The Netherlands, 1976. \endinput