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Strong Convergence Algorithms of the Split Common Fixed Point Problem for Total Quasi‐Asymptotically Pseudocontractive Operators

Author

Listed:
  • Peiyuan Wang
  • Hy Zhou

Abstract

We present a new algorithm for solving the two‐set split common fixed point problem with total quasi‐asymptotically pseudocontractive operators and consider the case of quasi‐pseudocontractive operators. Under some appropriate conditions, we prove that the proposed algorithms have strong convergence. The results presented in this paper improve and extend the previous algorithms and results of Censor and Segal (2009), Moudafi (2011 and 2010), Mohammed (2013), Yang et al. (2011), Chang et al. (2012), and others.

Suggested Citation

  • Peiyuan Wang & Hy Zhou, 2014. "Strong Convergence Algorithms of the Split Common Fixed Point Problem for Total Quasi‐Asymptotically Pseudocontractive Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:309368
    DOI: 10.1155/2014/309368
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    References listed on IDEAS

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    1. Shih-Sen Chang & Yeol Je Cho & J. K. Kim & W. B. Zhang & L. Yang, 2012. "Multiple‐Set Split Feasibility Problems for Asymptotically Strict Pseudocontractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Cuijie Zhang & Songnian He, 2012. "Strong Convergence Theorems for the Split Common Fixed Point Problem for Countable Family of Nonexpansive Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. S. S. Chang & L. Wang & Y. K. Tang & L. Yang, 2012. "The Split Common Fixed Point Problem for Total Asymptotically Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, December.
    4. Jing Na & Lin Wang & Zhaoli Ma, 2012. "The Split Common Fixed Point Problem for Quasi-Total Asymptotically Nonexpansive Uniformly Lipschitzian Mappings," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, May.
    5. S. S. Chang & L. Wang & Y. K. Tang & L. Yang, 2012. "The Split Common Fixed Point Problem for Total Asymptotically Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Cuijie Zhang & Songnian He, 2012. "Strong Convergence Theorems for the Split Common Fixed Point Problem for Countable Family of Nonexpansive Operators," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-11, July.
    7. Yanrong Yu & Delei Sheng, 2012. "On the Strong Convergence of an Algorithm about Firmly Pseudo-Demicontractive Mappings for the Split Common Fixed-Point Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, May.
    8. Gendai Gu & Shenghua Wang & Yeol Je Cho, 2011. "Strong Convergence Algorithms for Hierarchical Fixed Points Problems and Variational Inequalities," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-17, September.
    9. Shih-Sen Chang & Yeol Je Cho & J. K. Kim & W. B. Zhang & L. Yang, 2012. "Multiple-Set Split Feasibility Problems for Asymptotically Strict Pseudocontractions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, February.
    10. Gendai Gu & Shenghua Wang & Yeol Je Cho, 2011. "Strong Convergence Algorithms for Hierarchical Fixed Points Problems and Variational Inequalities," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    11. Yanrong Yu & Delei Sheng, 2012. "On the Strong Convergence of an Algorithm about Firmly Pseudo‐Demicontractive Mappings for the Split Common Fixed‐Point Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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