Article
| Title: | Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces (English) |
| Author: | Tang, Yan |
| Author: | Promkam, Ratthaprom |
| Author: | Cholamjiak, Prasit |
| Author: | Sunthrayuth, Pongsakorn |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 67 |
| Issue: | 2 |
| Year: | 2022 |
| Pages: | 129-152 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The aim of this paper is to propose two modified forward-backward splitting algorithms for zeros of the sum of a maximal monotone operator and a Bregman inverse strongly monotone operator in reflexive Banach spaces. We prove weak and strong convergence theorems of the generated sequences by the proposed methods under some suitable conditions. We apply our results to study the variational inequality problem and the equilibrium problem. Finally, a numerical example is given to illustrate the proposed methods. The results presented in this paper improve and generalize many known results in recent literature. (English) |
| Keyword: | maximal operator |
| Keyword: | Bregman distance |
| Keyword: | reflexive Banach space |
| Keyword: | weak convergence |
| Keyword: | strong convergence |
| MSC: | 47H05 |
| MSC: | 47H09 |
| MSC: | 47H10 |
| MSC: | 47J05 |
| MSC: | 47J25 |
| idZBL: | Zbl 07511498 |
| idMR: | MR4396681 |
| DOI: | 10.21136/AM.2021.0108-20 |
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| Date available: | 2022-03-25T08:21:01Z |
| Last updated: | 2022-09-06 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/149563 |
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