Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems
In this article, we introduce cyclic relatively nonexpansive mappings with respect to orbits and prove that every cyclic relatively nonexpansive mapping with respect to orbits T satisfying TA⊆B,TB⊆A has a best proximity point. We also prove that Mann’s iteration process for a noncyclic relatively no...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6676660 |
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| author | Laishram Shanjit Yumnam Rohen K. Anthony Singh |
| author_facet | Laishram Shanjit Yumnam Rohen K. Anthony Singh |
| author_sort | Laishram Shanjit |
| collection | DOAJ |
| description | In this article, we introduce cyclic relatively nonexpansive mappings with respect to orbits and prove that every cyclic relatively nonexpansive mapping with respect to orbits T satisfying TA⊆B,TB⊆A has a best proximity point. We also prove that Mann’s iteration process for a noncyclic relatively nonexpansive mapping with respect to orbits converges to a fixed point. These relatively nonexpansive mappings with respect to orbits need not be continuous. Some illustrations are given in support of our results. |
| format | Article |
| id | doaj-art-07d4a6eeab4b4400a0bac512e76f0b91 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-07d4a6eeab4b4400a0bac512e76f0b912025-08-20T03:55:28ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66766606676660Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point TheoremsLaishram Shanjit0Yumnam Rohen1K. Anthony Singh2Department of Mathematics, National Institute of Technology Manipur, Langol 795004, IndiaDepartment of Mathematics, National Institute of Technology Manipur, Langol 795004, IndiaDepartment of Mathematics, D. M. College of Science, Imphal, Manipur 795001, IndiaIn this article, we introduce cyclic relatively nonexpansive mappings with respect to orbits and prove that every cyclic relatively nonexpansive mapping with respect to orbits T satisfying TA⊆B,TB⊆A has a best proximity point. We also prove that Mann’s iteration process for a noncyclic relatively nonexpansive mapping with respect to orbits converges to a fixed point. These relatively nonexpansive mappings with respect to orbits need not be continuous. Some illustrations are given in support of our results.http://dx.doi.org/10.1155/2021/6676660 |
| spellingShingle | Laishram Shanjit Yumnam Rohen K. Anthony Singh Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems Journal of Mathematics |
| title | Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems |
| title_full | Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems |
| title_fullStr | Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems |
| title_full_unstemmed | Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems |
| title_short | Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems |
| title_sort | cyclic relatively nonexpansive mappings with respect to orbits and best proximity point theorems |
| url | http://dx.doi.org/10.1155/2021/6676660 |
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