On strong proximinality in normed linear spaces
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2016)
- Volume: 70, Issue: 1
- ISSN: 0365-1029
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topSahil Gupta, and T. D. Narang. "On strong proximinality in normed linear spaces." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 70.1 (2016): null. <http://eudml.org/doc/289805>.
@article{SahilGupta2016,
abstract = {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.},
author = {Sahil Gupta, T. D. Narang},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Strongly proximinal set; approximatively compact set; strongly Chebyshev set; compactly locally uniformly rotund space},
language = {eng},
number = {1},
pages = {null},
title = {On strong proximinality in normed linear spaces},
url = {http://eudml.org/doc/289805},
volume = {70},
year = {2016},
}
TY - JOUR
AU - Sahil Gupta
AU - T. D. Narang
TI - On strong proximinality in normed linear spaces
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2016
VL - 70
IS - 1
SP - null
AB - 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.
LA - eng
KW - Strongly proximinal set; approximatively compact set; strongly Chebyshev set; compactly locally uniformly rotund space
UR - http://eudml.org/doc/289805
ER -
References
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