On strong proximinality in normed linear spaces

Sahil Gupta, T. D. Narang

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.

Keywords


Strongly proximinal set; approximatively compact set; strongly Chebyshev set; compactly locally uniformly rotund space

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References


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DOI: http://dx.doi.org/10.17951/a.2016.70.1.19
Date of publication: 2016-07-04 15:43:59
Date of submission: 2016-07-01 19:40:39


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