Abstract
We introduce a concept of complete proximal normal structure and used to investigate the existence of a best proximity point for an arbitrary family of cyclic relatively nonexpansive mappings in the setting of strictly convex Banach spaces. We also prove that every bounded, closed and convex pair in uniformly convex Banach spaces as well as every compact and convex pairs in Banach spaces has complete proximal normal structure. Furthermore, we consider a class of cyclic relatively nonexpansive mappings in the sense of Suzuki and establish a new best proximity point theorem in the setting of Hilbert spaces.
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The authors would like to thank the anonymous referee for the careful reading of the manuscript and many useful comments.
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Communicated by Patrick Dowling.
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Gabeleh, M., Markin, J. Common best proximity pairs via the concept of complete proximal normal structure. Ann. Funct. Anal. 11, 831–847 (2020). https://doi.org/10.1007/s43034-020-00057-x
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DOI: https://doi.org/10.1007/s43034-020-00057-x
Keywords
- Best proximity pair
- Complete proximal normal structure
- Uniformly convex Banach space
- Relatively nonexpansive mapping