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Approximating Common Fixed Points of One-step Iterative Scheme with Error for Asymptotically Quasi-nonexpansive Type Nonself-Mappings

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In this paper, a new one-step iterative scheme with error for approximating common xed points of asymptotically quasi-nonexpansive type nonself mappings in Banach space is de ned. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al.,(2007), namely, A new iterative algorithm for approximating common xed points for asymptotically nonexpansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others.

Abstract

In this paper, a new one-step iterative scheme with error for approximating common xed points of asymptotically quasi-nonexpansive type nonself mappings in Banach space is de ned. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al.,(2007), namely, A new iterative algorithm for approximating common xed points for asymptotically nonexpansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others.

참고문헌 (8)

  1. S. S. Chang, "Approximating xed points of asymptoti- cally quasi-nonexpansive type mappings by the Ishikawa iterative sequences with mixed errors", Dynamic Systems and Applications, 13, pp.179~186 (2004)
  2. W. Nilsrakoo, "A new three-step xed point iteration scheme for asymp- totically nonexpansive mapping", Applied Mathematics and Computation, 181, pp.1026~1034 (2006)
  3. J. Quan, "Approximation common xed point asymptot- ically quasi-nonexpansive type mappings by the nite steps iterative sequences", Fixed Point Theory and Applications, 2006, pp.8~ (2006)
  4. Robert E. Megginson, "An Introduction to Banach Space Theory" (1998), Springer-Verlag
  5. D. R. Sahu, "Fixed point iteration processes for non-Lipschitzian map- pings of asymptotically quasi-nonexpansive type", International Journal of Mathematics and Mathematical Sciences, 2003, pp.2075~2081 (2003)
  6. J. Schu, "Iterative construction of xed point of asymptotically nonexpansive mappings", Journal of Mathematical Analysis and Applications, 158, pp.407~413 (1991)
  7. K. K. Tan, "Approximating xed points of nonexpansive mapping by the Ishikawa iteration process", Journal of Mathematical Analysis and Applications, 178, pp.301~308 (1993)
  8. H. Y. Zhou, "A new iterative algorithm for approximating common xed points for asymptotically nonexpansive mappings", Fixed Point Theory and Applications, 2007, pp.10~ (2007)

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