Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems

Laishram Shanjit, Yumnam Rohen, K. Anthony Singh and Ali Jaballah

Journal of Mathematics, 2021, vol. 2021, 1-7

Abstract: In this article, we introduce cyclic relatively nonexpansive mappings with respect to orbits and prove that every cyclic relatively nonexpansive mapping with respect to orbits T satisfying TA⊆B,TB⊆A has a best proximity point. We also prove that Mann’s iteration process for a noncyclic relatively nonexpansive mapping with respect to orbits converges to a fixed point. These relatively nonexpansive mappings with respect to orbits need not be continuous. Some illustrations are given in support of our results.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6676660

DOI: 10.1155/2021/6676660

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