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Mann-type algorithms for solving the monotone inclusion problem and the fixed point problem in reflexive Banach spaces

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Abstract

In this paper, we introduce two algorithms for finding a common solution of the monotone inclusion problem and the fixed point problem for a relatively nonexpansive mapping in reflexive Banach spaces. The weak convergence results for both algorithms are established without the prior knowledge of the Lipschitz constant of the mapping. An application to the variational inequality problem is considered. Finally, some numerical experiments of the proposed algorithms including comparisons with other algorithms are provided.

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Acknowledgements

The authors wish to thank editor and reviewers for value comments for improving the original manuscript. P. Sunthrayuth would like to thank Rajamangala University of Technology Thanyaburi (RMUTT). This work was supported by Thailand Science Research and Innovation under the project IRN62W0007, the revenue budget in 2021, School of Science, University of Phayao and Thailand Research Fund under project RSA6180084.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani, 12110, Thailand

    Pongsakorn Sunthrayuth

  2. School of Science, University of Phayao, Phayao, 56000, Thailand

    Nattawut Pholasa & Prasit Cholamjiak

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  1. Pongsakorn Sunthrayuth
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  2. Nattawut Pholasa
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Correspondence to Prasit Cholamjiak.

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Sunthrayuth, P., Pholasa, N. & Cholamjiak, P. Mann-type algorithms for solving the monotone inclusion problem and the fixed point problem in reflexive Banach spaces. Ricerche mat 72, 63–90 (2023). https://doi.org/10.1007/s11587-021-00596-y

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