Convergence Theorems for Two Simultaneous Quasinonexpansive Mappings in Banach Spaces
We discuss the approximation method of finding a common fixed point of two certain mappings defined on a Banach space. This paper deals with three modes of convergence, namely, weak, strong, and △-convergences in the presence of the uniform convexity of the norm. It is worth mentioning that the △-co...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/6629053 |
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| author | Satit Saejung Pongsakorn Yotkaew |
| author_facet | Satit Saejung Pongsakorn Yotkaew |
| author_sort | Satit Saejung |
| collection | DOAJ |
| description | We discuss the approximation method of finding a common fixed point of two certain mappings defined on a Banach space. This paper deals with three modes of convergence, namely, weak, strong, and △-convergences in the presence of the uniform convexity of the norm. It is worth mentioning that the △-convergence which is closely connected with the weak convergence is discussed without assuming the Opial’s condition. Our results not only generalize the results recently announced by Garodia et al. but also rectify a gap in their paper. Finally, some concrete numerical examples are shown that our results are genuine generalizations of a number of results in the literature. |
| format | Article |
| id | doaj-art-167ce79862094ce3b6798ae2a1e0d917 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-167ce79862094ce3b6798ae2a1e0d9172025-02-03T05:42:22ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/6629053Convergence Theorems for Two Simultaneous Quasinonexpansive Mappings in Banach SpacesSatit Saejung0Pongsakorn Yotkaew1Department of MathematicsDepartment of MathematicsWe discuss the approximation method of finding a common fixed point of two certain mappings defined on a Banach space. This paper deals with three modes of convergence, namely, weak, strong, and △-convergences in the presence of the uniform convexity of the norm. It is worth mentioning that the △-convergence which is closely connected with the weak convergence is discussed without assuming the Opial’s condition. Our results not only generalize the results recently announced by Garodia et al. but also rectify a gap in their paper. Finally, some concrete numerical examples are shown that our results are genuine generalizations of a number of results in the literature.http://dx.doi.org/10.1155/2024/6629053 |
| spellingShingle | Satit Saejung Pongsakorn Yotkaew Convergence Theorems for Two Simultaneous Quasinonexpansive Mappings in Banach Spaces Journal of Mathematics |
| title | Convergence Theorems for Two Simultaneous Quasinonexpansive Mappings in Banach Spaces |
| title_full | Convergence Theorems for Two Simultaneous Quasinonexpansive Mappings in Banach Spaces |
| title_fullStr | Convergence Theorems for Two Simultaneous Quasinonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | Convergence Theorems for Two Simultaneous Quasinonexpansive Mappings in Banach Spaces |
| title_short | Convergence Theorems for Two Simultaneous Quasinonexpansive Mappings in Banach Spaces |
| title_sort | convergence theorems for two simultaneous quasinonexpansive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2024/6629053 |
| work_keys_str_mv | AT satitsaejung convergencetheoremsfortwosimultaneousquasinonexpansivemappingsinbanachspaces AT pongsakornyotkaew convergencetheoremsfortwosimultaneousquasinonexpansivemappingsinbanachspaces |