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Iterative Algorithms for Split Common Fixed Point Problem Involved in Pseudo-Contractive Operators without Lipschitz Assumption

Author

Listed:
  • Jinzuo Chen

    (School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, China)

  • Mihai Postolache

    (Center for General Education, China Medical University, Taichung 40402, Taiwan
    Romanian Academy, Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, 050711 Bucharest, Romania
    Department of Mathematics and Informatics, University “Politehnica” of Bucharest, 060042 Bucharest, Romania)

  • Li-Jun Zhu

    (The Key Laboratory of Intelligent Information and Big Data Processing of NingXia Province, North Minzu University, Yinchuan 750021, China)

Abstract

Two iterative algorithms are suggested for approximating a solution of the split common fixed point problem involved in pseudo-contractive operators without Lipschitz assumption. We prove that the sequence generated by the first algorithm converges weakly to a solution of the split common fixed point problem and the second one converges strongly. Moreover, the sequence { x n } generated by Algorithm 3 strongly converges to z = proj S 0 , which is the minimum-norm solution of problem (1). Numerical examples are included.

Suggested Citation

  • Jinzuo Chen & Mihai Postolache & Li-Jun Zhu, 2019. "Iterative Algorithms for Split Common Fixed Point Problem Involved in Pseudo-Contractive Operators without Lipschitz Assumption," Mathematics, MDPI, vol. 7(9), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:777-:d:260402
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    References listed on IDEAS

    as
    1. Andrzej Cegielski, 2015. "General Method for Solving the Split Common Fixed Point Problem," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 385-404, May.
    2. L. C. Ceng & A. Petruşel & J. C. Yao, 2013. "Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-25, March.
    3. Yonghong Yao & Yeong-Cheng Liou & Naseer Shahzad, 2012. "A Strongly Convergent Method for the Split Feasibility Problem," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, October.
    4. Zhao-Rong Kong & Lu-Chuan Ceng & Ching-Feng Wen, 2012. "Some Modified Extragradient Methods for Solving Split Feasibility and Fixed Point Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-32, December.
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    Cited by:

    1. Thidaporn Seangwattana & Somyot Plubtieng & Kanokwan Sitthithakerngkiet, 2021. "A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 614-628, June.

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