Some Results on Iterative Proximal Convergence and Chebyshev Center

摘要

In this paper, we prove a sufficient condition that every nonempty closed convex bounded pair in a reflexive Banach space satisfying Opial’s condition has proximal normal structure. We analyze the relatively nonexpansive self-mapping on satisfying and , to show that Ishikawa’s and Halpern’s iteration converges to the best proximity point. Also, we prove that under relatively isometry self-mapping on satisfying and , Ishikawa’s iteration converges to the best proximity point in the collection of all Chebyshev centers of relative to . Some illustrative examples are provided to support our results.