Some Results on Iterative Proximal Convergence and Chebyshev Center

Autor: Laishram Shanjit, Yumnam Rohen, Sumit Chandok, M. Bina Devi
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Journal of Function Spaces, Vol 2021 (2021)
Druh dokumentu: article
ISSN: 2314-8896
2314-8888
DOI: 10.1155/2021/8863325
Popis: 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.
Databáze: Directory of Open Access Journals
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