A characterization of weak proximal normal structure and best proximity pairs

A characterization of weak proximal normal structure and best proximity pairs

The aim of this paper is to address an open problem given in [Kirk et al. in J Math Anal Appl 463:461–476, (2018)]. We give a characterization of weak proximal normal structure using best proximity pair property. We also introduce a notion of pointwise cyclic contraction wrt orbits and therein prove...

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Veröffentlicht in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2022-04, Vol.116 (2), Article 80
Hauptverfasser: Digar, Abhik, García, Rafael Espínola, Kosuru, G. Sankara Raju
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Banach spaces
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Proximity
Theoretical
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Zusammenfassung:The aim of this paper is to address an open problem given in [Kirk et al. in J Math Anal Appl 463:461–476, (2018)]. We give a characterization of weak proximal normal structure using best proximity pair property. We also introduce a notion of pointwise cyclic contraction wrt orbits and therein prove the existence of a best proximity pair in the setting of reflexive Banach spaces.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-022-01217-5