General modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete CAT(0) $\operatorname{CAT}(0)$ spaces
Abstract It is well known that the concept (generalized) asymptotically nonexpansive is closely related to the theory of fixed points in Banach spaces, and the implicit midpoint rule is one of the powerful numerical methods for solving differential equations. The purpose of this paper is to introduc...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-2114-7 |
| _version_ | 1819226658061680640 |
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| author | Ting-jian Xiong Heng-you Lan |
| author_facet | Ting-jian Xiong Heng-you Lan |
| author_sort | Ting-jian Xiong |
| collection | DOAJ |
| description | Abstract It is well known that the concept (generalized) asymptotically nonexpansive is closely related to the theory of fixed points in Banach spaces, and the implicit midpoint rule is one of the powerful numerical methods for solving differential equations. The purpose of this paper is to introduce a class of new general modified viscosity implicit rules of generalized asymptotically nonexpansive mappings in complete CAT(0) $\operatorname{CAT}(0)$ spaces, and to prove some strong convergence theorems of the procedure generated by the new general modified viscosity implicit rules under some suitable conditions. The results presented in this paper improve and extend varieties of results in the recent literature. |
| first_indexed | 2024-12-23T10:28:59Z |
| format | Article |
| id | doaj.art-3c1fa17bf4d34a409d82a7b506eb3a45 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-23T10:28:59Z |
| publishDate | 2019-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-3c1fa17bf4d34a409d82a7b506eb3a452022-12-21T17:50:29ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-06-012019111610.1186/s13660-019-2114-7General modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete CAT(0) $\operatorname{CAT}(0)$ spacesTing-jian Xiong0Heng-you Lan1College of Mathematics and Statistics, Sichuan University of Science & EngineeringCollege of Mathematics and Statistics, Sichuan University of Science & EngineeringAbstract It is well known that the concept (generalized) asymptotically nonexpansive is closely related to the theory of fixed points in Banach spaces, and the implicit midpoint rule is one of the powerful numerical methods for solving differential equations. The purpose of this paper is to introduce a class of new general modified viscosity implicit rules of generalized asymptotically nonexpansive mappings in complete CAT(0) $\operatorname{CAT}(0)$ spaces, and to prove some strong convergence theorems of the procedure generated by the new general modified viscosity implicit rules under some suitable conditions. The results presented in this paper improve and extend varieties of results in the recent literature.http://link.springer.com/article/10.1186/s13660-019-2114-7General modified viscosity implicit ruleFixed pointStrong convergenceGeneralized asymptotically nonexpansive mappingCAT ( 0 ) $\operatorname{CAT}(0)$ space |
| spellingShingle | Ting-jian Xiong Heng-you Lan General modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete CAT(0) $\operatorname{CAT}(0)$ spaces Journal of Inequalities and Applications General modified viscosity implicit rule Fixed point Strong convergence Generalized asymptotically nonexpansive mapping CAT ( 0 ) $\operatorname{CAT}(0)$ space |
| title | General modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete CAT(0) $\operatorname{CAT}(0)$ spaces |
| title_full | General modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete CAT(0) $\operatorname{CAT}(0)$ spaces |
| title_fullStr | General modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete CAT(0) $\operatorname{CAT}(0)$ spaces |
| title_full_unstemmed | General modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete CAT(0) $\operatorname{CAT}(0)$ spaces |
| title_short | General modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete CAT(0) $\operatorname{CAT}(0)$ spaces |
| title_sort | general modified viscosity implicit rules for generalized asymptotically nonexpansive mappings in complete cat 0 operatorname cat 0 spaces |
| topic | General modified viscosity implicit rule Fixed point Strong convergence Generalized asymptotically nonexpansive mapping CAT ( 0 ) $\operatorname{CAT}(0)$ space |
| url | http://link.springer.com/article/10.1186/s13660-019-2114-7 |
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