Study of minimal invariant pairs for relatively nonexpansive mappings with respect to orbits

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 or...

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Bibliographic Details
Published in:Optimization 2021-06, Vol.70 (5-6), p.1029-1045
Main Authors: Gabeleh, M., Moshokoa, S. P.
Format: Article
Language:English
Subjects:
Banach spaces
Best proximity pair
Invariants
noncyclic relatively mapping w.r.t. orbits
Orbits
strictly convex Banach space
Structural analysis
T-regular pair
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Summary: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.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1745797