The paper deals with strong proximinality in normed linear spaces. It is proved that in a compactly locally uniformly rotund Banach space, proximinality, strong proximinality, weak approximative compactness and approximative compactness are all equivalent for closed convex sets. How strong proximinality can be transmitted to and from quotient spaces has also been discussed.
@article{bwmeta1.element.ojs-doi-10_17951_a_2016_70_1_19,
author = {Sahil Gupta and T. D. Narang},
title = {On strong proximinality in normed linear spaces},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {70},
year = {2016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2016_70_1_19}
}
Sahil Gupta; T. D. Narang. On strong proximinality in normed linear spaces. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 70 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2016_70_1_19/
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