A Characterization of Weak Proximal Normal Structure and Best Proximity Pairs
Functional Analysis
2022-01-27 v1
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. {\bf{vol 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.
Keywords
Cite
@article{arxiv.2201.10767,
title = {A Characterization of Weak Proximal Normal Structure and Best Proximity Pairs},
author = {Abhik Digar and Rafael Espínola García and G. Sankara Raju Kosuru},
journal= {arXiv preprint arXiv:2201.10767},
year = {2022}
}