Some Results on Iterative Proximal Convergence and Chebyshev Center
In this paper, we prove a sufficient condition that every nonempty closed convex bounded pair M,N in a reflexive Banach space B satisfying Opial’s condition has proximal normal structure. We analyze the relatively nonexpansive self-mapping T on M∪N satisfying TM⊆M and TN⊆N, to show that Ishikawa’s a...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/8863325 |
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| author | Laishram Shanjit Yumnam Rohen Sumit Chandok M. Bina Devi |
| author_facet | Laishram Shanjit Yumnam Rohen Sumit Chandok M. Bina Devi |
| author_sort | Laishram Shanjit |
| collection | DOAJ |
| description | In this paper, we prove a sufficient condition that every nonempty closed convex bounded pair M,N in a reflexive Banach space B satisfying Opial’s condition has proximal normal structure. We analyze the relatively nonexpansive self-mapping T on M∪N satisfying TM⊆M and TN⊆N, to show that Ishikawa’s and Halpern’s iteration converges to the best proximity point. Also, we prove that under relatively isometry self-mapping T on M∪N satisfying TN⊆N and TM⊆M, Ishikawa’s iteration converges to the best proximity point in the collection of all Chebyshev centers of N relative to M. Some illustrative examples are provided to support our results. |
| format | Article |
| id | doaj-art-5a8d7fa0dc8f40f0ad49d08407a7f7d6 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-5a8d7fa0dc8f40f0ad49d08407a7f7d62025-02-03T06:05:45ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/88633258863325Some Results on Iterative Proximal Convergence and Chebyshev CenterLaishram Shanjit0Yumnam Rohen1Sumit Chandok2M. Bina Devi3Department of Mathematics, NIT Manipur, Langol 795004, IndiaDepartment of Mathematics, NIT Manipur, Langol 795004, IndiaSchool of Mathematics, Thapar Institute of Engineering & Technology, Patiala 147004, IndiaDepartment of Mathematics, DM College of Science Manipur, Imphal 795001, IndiaIn this paper, we prove a sufficient condition that every nonempty closed convex bounded pair M,N in a reflexive Banach space B satisfying Opial’s condition has proximal normal structure. We analyze the relatively nonexpansive self-mapping T on M∪N satisfying TM⊆M and TN⊆N, to show that Ishikawa’s and Halpern’s iteration converges to the best proximity point. Also, we prove that under relatively isometry self-mapping T on M∪N satisfying TN⊆N and TM⊆M, Ishikawa’s iteration converges to the best proximity point in the collection of all Chebyshev centers of N relative to M. Some illustrative examples are provided to support our results.http://dx.doi.org/10.1155/2021/8863325 |
| spellingShingle | Laishram Shanjit Yumnam Rohen Sumit Chandok M. Bina Devi Some Results on Iterative Proximal Convergence and Chebyshev Center Journal of Function Spaces |
| title | Some Results on Iterative Proximal Convergence and Chebyshev Center |
| title_full | Some Results on Iterative Proximal Convergence and Chebyshev Center |
| title_fullStr | Some Results on Iterative Proximal Convergence and Chebyshev Center |
| title_full_unstemmed | Some Results on Iterative Proximal Convergence and Chebyshev Center |
| title_short | Some Results on Iterative Proximal Convergence and Chebyshev Center |
| title_sort | some results on iterative proximal convergence and chebyshev center |
| url | http://dx.doi.org/10.1155/2021/8863325 |
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