A Characterization of Weak Proximal Normal Structure and Best Proximity Pairs

2022/01/26 by Digar, Abhik, García, Rafael Espínola, Kosuru, G. Sankara Raju · 1 citation
#46E15 #47H10 #54H25 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2201.10767

Abstract

The aim of this paper is to address an open problem given in [Kirk, W. A., Shahzad, Naseer, Normal structure and orbital fixed point conditions, J. Math. Anal. Appl. \bfvol 463(2), (2018) 461--476]. 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.

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• Best Proximity Point Results for Cyclic Orbital Contraction Mappings in CAT_p(0) Metric Spaces

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