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Self-adaptive Forward–Backward Contraction-type Methods for Generalized Split Feasibility Problems

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Abstract

Based on the recent important results of Takahashi–Xu–Yao [Set-Valued and Variational Analysis 23(2015), 205–221] and other related results on split feasibility problems, we study a certain class of generalized split feasibility problems which includes many other split-type problems. We propose some new self-adaptive forward–backward contraction-type methods and prove that they converge strongly to a minimum-norm solution of the generalized split feasibility problems in real Hilbert spaces. As a by-product, we obtain self-adaptive methods for solving other classes of generalized split feasibility problems in real Hilbert spaces. Finally, we apply our results to solve an optimal control problem and an image restoration problem through numerical implementations, and compare our methods with related strongly convergent methods in the literature.

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Acknowledgements

The authors thank the reviewer for the time spent and efforts made to read through the manuscript and for his/her constructive comments, questions and suggestions, which have helped to improve the quality of the article.

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Authors and Affiliations

  1. Department of Mathematics, The Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Chinedu Izuchukwu

  2. School of Mathematical Sciences, University of Southampton, SO17 1BJ, Southampton, United Kingdom

    Lateef Olakunle Jolaoso

  3. Department of Mathematics and Statistics, Auburn University, Alabama, AL 36849, USA

    Monday Ogudu Nnakwe

  4. Department of Mathematics, University of Eswatini, Private Bag, Kwaluseni, Eswatini

    Godwin Chidi Ugwunnadi

  5. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Abdul Rahim Khan

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  1. Chinedu Izuchukwu
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  2. Lateef Olakunle Jolaoso
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  5. Abdul Rahim Khan
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Correspondence to Chinedu Izuchukwu.

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Izuchukwu, C., Jolaoso, L.O., Nnakwe, M.O. et al. Self-adaptive Forward–Backward Contraction-type Methods for Generalized Split Feasibility Problems. Mediterr. J. Math. 19, 204 (2022). https://doi.org/10.1007/s00009-022-02114-2

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  • DOI: https://doi.org/10.1007/s00009-022-02114-2

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