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Strong Convergence Theorems of Viscosity Iterative Algorithms for Split Common Fixed Point Problems

Author

Listed:
  • Peichao Duan

    (College of Science, Civil Aviation University of China, Tianjin 300300, China)

  • Xubang Zheng

    (College of Science, Civil Aviation University of China, Tianjin 300300, China)

  • Jing Zhao

    (College of Science, Civil Aviation University of China, Tianjin 300300, China)

Abstract

In this paper, we propose a viscosity approximation method to solve the split common fixed point problem and consider the bounded perturbation resilience of the proposed method in general Hilbert spaces. Under some mild conditions, we prove that our algorithms strongly converge to a solution of the split common fixed point problem, which is also the unique solution of the variational inequality problem. Finally, we show the convergence and effectiveness of the algorithms by two numerical examples.

Suggested Citation

  • Peichao Duan & Xubang Zheng & Jing Zhao, 2018. "Strong Convergence Theorems of Viscosity Iterative Algorithms for Split Common Fixed Point Problems," Mathematics, MDPI, vol. 7(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2018:i:1:p:14-:d:192986
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    References listed on IDEAS

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    1. Hong-Kun Xu, 2011. "Averaged Mappings and the Gradient-Projection Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 360-378, August.
    2. Wenma Jin & Yair Censor & Ming Jiang, 2016. "Bounded perturbation resilience of projected scaled gradient methods," Computational Optimization and Applications, Springer, vol. 63(2), pages 365-392, March.
    3. Yair Censor & Wei Chen & Patrick Combettes & Ran Davidi & Gabor Herman, 2012. "On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints," Computational Optimization and Applications, Springer, vol. 51(3), pages 1065-1088, April.
    4. Songnian He & Caiping Yang, 2013. "Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
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