Some Results on Iterative Proximal Convergence and Chebyshev Center. (7th January 2021) - Shanjit, Laishram; Rohen, Yumnam; Chandok, Sumit; Devi, M. Bina
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.