Study of minimal invariant pairs for relatively nonexpansive mappings with respect to orbits. (3rd June 2021)

• Record Type: Journal Article
• Authors: Gabeleh, M.; Moshokoa, S. P.
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 1029
• Page End: 1045
• Publication Date: 2021-06-03
• Subjects: Best proximity pair -- T-regular pair -- noncyclic relatively mapping w.r.t. orbits -- strictly convex Banach space; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1745797
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this article, we survey the existence of best proximity pairs for noncyclic contractions with respect to orbits which are defined on a non-convex and weakly compact pair of subsets of a strictly convex Banach space. We then consider the class of relatively nonexpansive mappings with respect to orbits and present a characterization for proximal normal structure. Finally, the structure of minimal invariant pairs under relatively nonexpansive mappings with respect to orbits will be studied. Our conclusions improve and extend the well-known results in the literature.