대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제24권4호
  • /
  • Pages.539-551
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  • 2009
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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STRONG CONVERGENCE OF MODIFIED HYBRID ALGORITHM FOR QUASI-φ-ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

  • Zhang, Huancheng (DEPARTMENT OF MATHEMATICS TIANJIN POLYTECHNIC UNIVERSITY) ;
  • Su, Yongfu (DEPARTMENT OF MATHEMATICS TIANJIN POLYTECHNIC UNIVERSITY)
  • 발행 : 2009.10.31
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초록

In this paper, we propose a modified hybrid algorithm and prove strong convergence theorems for a family of quasi-$\phi$-asymptotically nonexpansive mappings. Our results extend and improve the results by Nakajo, Takahashi, Kim, Xu, Su and some others.

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참고문헌

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  2. Ya. I. Alber and S. Reich, An iterative method for solving a class of nonlinear operator equations in Banach spaces, Panamer. Math. J. 4 (1994), 39-54
  3. M. Y. Carlos and H. K. Xu, Strong convergence of the CQ method for fixed point iteration process, Nonlinear Anal. 64 (2006), 2240–2411 https://doi.org/10.1016/j.na.2005.08.018
  4. I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer, Dordrecht, 1990
  5. K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174 https://doi.org/10.2307/2038462
  6. Y. Haugazeau, Sur les inequations variationnelles et la minimisation de fonctionnelles convexes, These, Universite de Paris, Paris, France.
  7. S. Kamimura and W. Takahashi, Strong convergence of a proximal-type algorithm in a Banach space, SIAM J. Optim. 13 (2002), 938–945 https://doi.org/10.1137/S105262340139611X
  8. T. H. Kim and H. K. Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64 (2006), 1140–1152 https://doi.org/10.1016/j.na.2005.05.059
  9. K. Nakajo and W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semi-groups, J. Math. Anal. Appl. 279 (2003), 372–379 https://doi.org/10.1016/S0022-247X(02)00458-4
  10. J. Schu, Iteration construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991), 407–413 https://doi.org/10.1016/0022-247X(91)90245-U
  11. Y. F. Su and X. L. Qin, Strong convergence of modified Ishikawa iterations for nonlinear mappings, Proc. Indian Acad. Sci.(Math.Sci.) 117 (2007), 97–107 https://doi.org/10.1007/s12044-007-0008-y
  12. W. Takahashi, Nonlinear Functional Analysis, Yokohama-Publishers, 2000.
  13. H. Y. Zhou, Y. J. Cho, and S. M. Kang, A new iterative algorithm for approximating common fixed points for asymptotically nonexpansive mappings, Fixed Point Theory and Applications 2007 (2007), doi:10.1155/2007/64874.

피인용 문헌

  1. Strong convergence theorems for nonlinear operator equations with total quasi-ϕ-asymptotically nonexpansive mappings and applications vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-1812-2012-34
  2. Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces vol.2012, 2012, https://doi.org/10.1155/2012/961560
  3. A New Hybrid Algorithm for Solving a System of Generalized Mixed Equilibrium Problems, Solving a Family of Quasi--Asymptotically Nonexpansive Mappings, and Obtaining Common Fixed Points in Banach Space vol.2011, 2011, https://doi.org/10.1155/2011/106323