Оn a proximal point algorithm for solving minimization problem and common fixed point problem in CAT($k$) spaces
UDC 517.9 We propose a new modified proximal point algorithm in the setting of CAT(1) spaces, which can be used for solving the minimization problem and the  common fixed-point problem.  In addition, we prove several convergence results for the pro...
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| Date: | 2023 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6770 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512511057461248 |
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| author | Garodia, C. Radenovic, S. Garodia, C. Radenovic, S. |
| author_facet | Garodia, C. Radenovic, S. Garodia, C. Radenovic, S. |
| author_sort | Garodia, C. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-03-06T14:27:01Z |
| description | UDC 517.9
We propose a new modified proximal point algorithm in the setting of CAT(1) spaces, which can be used for solving the minimization problem and the  common fixed-point problem.  In addition, we prove several convergence results for the proposed algorithm under certain mild conditions.  Further, we provide some applications for the convex minimization problem and the fixed point problem in the CAT($k$) spaces with a bounded positive real number $k$.  In the process, several relevant results available in the existing literature are generalized and improved. |
| doi_str_mv | 10.37863/umzh.v75i2.6770 |
| first_indexed | 2026-03-24T03:29:57Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6770 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:29:57Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-67702023-03-06T14:27:01Z Оn a proximal point algorithm for solving minimization problem and common fixed point problem in CAT($k$) spaces Оn a proximal point algorithm for solving minimization problem and common fixed point problem in CAT($k$) spaces Garodia, C. Radenovic, S. Garodia, C. Radenovic, S. Minimization problem; resolvent operator; CAT(1) space; proximal point algorithm; nonexpansive mapping. Mathematics UDC 517.9 We propose a new modified proximal point algorithm in the setting of CAT(1) spaces, which can be used for solving the minimization problem and the  common fixed-point problem.  In addition, we prove several convergence results for the proposed algorithm under certain mild conditions.  Further, we provide some applications for the convex minimization problem and the fixed point problem in the CAT($k$) spaces with a bounded positive real number $k$.  In the process, several relevant results available in the existing literature are generalized and improved. УДК 517.9 Про проксимальний точковий алгоритм для розв’язування задачі мінімізації  та спільної задачі про нерухому точку в просторах CAT($k$) Запропоновано новий модифікований проксимальний точковий алгоритм у постановці просторів CAT(1), який можна використовувати для розв'язування задачі мінімізації та спільної задачі про нерухому точку.  Крім того, доведено кілька результатів про збіжність запропонованого алгоритму за деяких слабких умов. Далі, наведено деякі застосування до задачі опуклої мінімізації та задачі про нерухому точку в просторах CAT($k$) з обмеженим додатним дійсним числом $k$.  У процесі узагальнено та вдосконалено кілька відповідних результатів, відомих з літератури. Institute of Mathematics, NAS of Ukraine 2023-03-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6770 10.37863/umzh.v75i2.6770 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 2 (2023); 168 - 181 Український математичний журнал; Том 75 № 2 (2023); 168 - 181 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6770/9794 Copyright (c) 2023 Chanchal Garodia, Stojan Radenovic |
| spellingShingle | Garodia, C. Radenovic, S. Garodia, C. Radenovic, S. Оn a proximal point algorithm for solving minimization problem and common fixed point problem in CAT($k$) spaces |
| title | Оn a proximal point algorithm for solving minimization problem and common fixed point problem in CAT($k$) spaces |
| title_alt | Оn a proximal point algorithm for solving minimization problem and common fixed point problem in CAT($k$) spaces |
| title_full | Оn a proximal point algorithm for solving minimization problem and common fixed point problem in CAT($k$) spaces |
| title_fullStr | Оn a proximal point algorithm for solving minimization problem and common fixed point problem in CAT($k$) spaces |
| title_full_unstemmed | Оn a proximal point algorithm for solving minimization problem and common fixed point problem in CAT($k$) spaces |
| title_short | Оn a proximal point algorithm for solving minimization problem and common fixed point problem in CAT($k$) spaces |
| title_sort | оn a proximal point algorithm for solving minimization problem and common fixed point problem in cat($k$) spaces |
| topic_facet | Minimization problem resolvent operator CAT(1) space proximal point algorithm nonexpansive mapping. Mathematics |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6770 |
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