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A strongly convergent algorithm for the split common fixed point problem

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  • Boikanyo, Oganeditse A.

Abstract

Recently, Cui and Wang (2014) constructed an algorithm for demicontractive operators that converges weakly, under mild assumptions, to some solution of the split common fixed point problem. In this paper, based on Halpern’s type method (1967), we construct an algorithm for demicontractive operators that produces sequences that always converge strongly to a specific solution of the split common fixed point problem. Particular cases of directed operators and quasi-nonexpansive mappings are also considered.

Suggested Citation

  • Boikanyo, Oganeditse A., 2015. "A strongly convergent algorithm for the split common fixed point problem," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 844-853.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:844-853
    DOI: 10.1016/j.amc.2015.05.130
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    References listed on IDEAS

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    1. Fenghui Wang & Huanhuan Cui, 2012. "On the contraction-proximal point algorithms with multi-parameters," Journal of Global Optimization, Springer, vol. 54(3), pages 485-491, November.
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    Cited by:

    1. Nishu Gupta & Mihai Postolache & Ashish Nandal & Renu Chugh, 2021. "A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm," Mathematics, MDPI, vol. 9(4), pages 1-19, February.
    2. Truong Minh Tuyen & Nguyen Thi Thu Thuy & Nguyen Minh Trang, 2019. "A Strong Convergence Theorem for a Parallel Iterative Method for Solving the Split Common Null Point Problem in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 271-291, October.
    3. Wachirapong Jirakitpuwapat & Poom Kumam & Yeol Je Cho & Kanokwan Sitthithakerngkiet, 2019. "A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing," Mathematics, MDPI, vol. 7(3), pages 1-20, February.
    4. Nattakarn Kaewyong & Kanokwan Sitthithakerngkiet, 2022. "An Inertial Extragradient Direction Method with Self-Adaptive Step Size for Solving Split Minimization Problems and Its Applications to Compressed Sensing," Mathematics, MDPI, vol. 10(6), pages 1-25, March.
    5. Ismat Beg & Mujahid Abbas & Muhammad Waseem Asghar, 2023. "Approximation of the Solution of Split Equality Fixed Point Problem for Family of Multivalued Demicontractive Operators with Application," Mathematics, MDPI, vol. 11(4), pages 1-16, February.

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