Study of minimal invariant pairs for relatively nonexpansive mappings with respect to orbits. (3rd June 2021) - Gabeleh, M.; Moshokoa, S. P.
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.