A Method of approximation for a zero of the sum of maximally monotone mappings in Hilbert spaces
Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is α-inverse strongly monotone is dispensed with. In addition, we give some applications to th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Emerald Publishing
2021-04-01
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| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1016/j.ajmsc.2019.05.004/full/pdf |
| Summary: | Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is α-inverse strongly monotone is dispensed with. In addition, we give some applications to the minimization problem. Our method of proof is of independent interest. Finally, a numerical example which supports our main result is presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings. |
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| ISSN: | 1319-5166 2588-9214 |