Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces

Y. Shehu, Results in Mathematics 74 (2019) 138.

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Abstract
It is well known that many problems in image recovery, signal processing, and machine learning can be modeled as finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. Many papers have studied forward-backward splitting methods for finding zeros of the sum of two monotone operators in Hilbert spaces. Most of the proposed splitting methods in the literature have been proposed for the sum of maximal monotone and inverse-strongly monotone operators in Hilbert spaces. In this paper, we consider splitting methods for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators in Banach spaces. We obtain weak and strong convergence results for the zeros of the sum of maximal monotone and Lipschitz continuous monotone operators in Banach spaces. Many already studied problems in the literature can be considered as special cases of this paper.
Publishing Year
Date Published
2019-06-29
Journal Title
Results in Mathematics
Volume
74
Issue
4
Article Number
138
ISSN
eISSN
IST-REx-ID

Cite this

Shehu Y. Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. 2019;74(4):138. doi:10.1007/s00025-019-1061-4
Shehu, Y. (2019). Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics, 74(4), 138. https://doi.org/10.1007/s00025-019-1061-4
Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum of Monotone Operators in Banach Spaces.” Results in Mathematics 74, no. 4 (2019): 138. https://doi.org/10.1007/s00025-019-1061-4.
Y. Shehu, “Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces,” Results in Mathematics, vol. 74, no. 4, p. 138, 2019.
Shehu Y. 2019. Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces. Results in Mathematics. 74(4), 138.
Shehu, Yekini. “Convergence Results of Forward-Backward Algorithms for Sum of Monotone Operators in Banach Spaces.” Results in Mathematics, vol. 74, no. 4, Springer, 2019, p. 138, doi:10.1007/s00025-019-1061-4.
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