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The Split Feasibility Problem with Multiple Output Sets for Demicontractive Mappings

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Abstract

In Hilbert spaces, we study the split feasibility problem with multiple output sets for demicontractive mappings. For solving this problem, we propose an iterative method and construct two selection strategies of stepsizes, namely the fixed stepsize and the variable stepsize. Under appropriate conditions, we prove the weak convergence of the proposed iterative method and the strong convergence of its variant. Furthermore, the experimental results show that the stepsize we constructed is very helpful to improve the convergence speed of the iterative method.

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Acknowledgements

Many thanks to the reviewers for their valuable comments and suggestions, which helped us improve the quality of the manuscript. This work was supported by the National Natural Science Foundation of China (No. 11971216).

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Authors and Affiliations

  1. Department of Mathematics, Luoyang Normal University, Luoyang, 471934, China

    Fenghui Wang

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  1. Fenghui Wang
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Correspondence to Fenghui Wang.

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Communicated by Irena Lasiecka.

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Wang, F. The Split Feasibility Problem with Multiple Output Sets for Demicontractive Mappings. J Optim Theory Appl 195, 837–853 (2022). https://doi.org/10.1007/s10957-022-02096-x

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