Some Results on Iterative Proximal Convergence and Chebyshev Center. (7th January 2021)

• Record Type: Journal Article
• Authors: Shanjit, Laishram; Rohen, Yumnam; Chandok, Sumit; Devi, M. Bina
• Other Names: Mitrovic Zoran Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-01-07
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/8863325
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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 T M ⊆ M and T N ⊆ 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 T N ⊆ N and T M ⊆ 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.