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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |