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Solving the Split Feasibility Problem and the Fixed Point Problem of Left Bregman Firmly Nonexpansive Mappings via the Dynamical Step Sizes in Banach Spaces

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Abstract

In this work, we suggest a new self-adaptive method using the dynamical step size technique for solving the split feasibility problem and the fixed point problem of left Bregman firmly nonexpansive mappings in a certain Banach space. We establish the strong convergence without the computation of the operator norms. Finally, we give some examples including its numerical experiments to show the efficiency and the implementation of our proposed method.

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Acknowledgements

The authors would like to thank reviewers and editor for their comments on the manuscript which helped us very much in improving and presenting the original version of this paper. This work is supported by Thailand Research Fund and University of Phayao under the project RSA6180084 and UOE62001. This work was partially supported by Thailand Science Research and Innovation under the project IRN62W0007.

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

    N. Pholasa, K. Kankam & P. Cholamjiak

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  1. N. Pholasa
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  2. K. Kankam
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  3. P. Cholamjiak
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Correspondence to P. Cholamjiak.

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Pholasa, N., Kankam, K. & Cholamjiak, P. Solving the Split Feasibility Problem and the Fixed Point Problem of Left Bregman Firmly Nonexpansive Mappings via the Dynamical Step Sizes in Banach Spaces. Vietnam J. Math. 49, 1011–1026 (2021). https://doi.org/10.1007/s10013-020-00384-5

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  • DOI: https://doi.org/10.1007/s10013-020-00384-5

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