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Advances in Inequalities and Applications ISSN 2050-7461

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Adv. Inequal. Appl. 2018 (2018), Article ID 9

Some new results on certain types of proximinality in Banach spaces

S. Alsuradi, R. Khalil

PDF (128.0 KB) https://doi.org/10.28919/aia/3649

Abstract

In this paper, we prove that any convex set in a normed space is $\varepsilon -$proximinal. Consequently, every subspace in a Banach space is $\varepsilon -$proximinal. Some other results of proximinality in tensor product spaces are given.

Published
4 June 2018
Volume
2018 (2018)
License
CC BY 3.0

Copyright © 2018 S. Alsuradi, R. Khalil. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

S. Alsuradi, R. Khalil, Some new results on certain types of proximinality in Banach spaces, Adv. Inequal. Appl. 2018 (2018), 9. https://doi.org/10.28919/aia/3649

BibTeX
@article{Alsuradi2018,
  author  = {Alsuradi, S. and Khalil, R.},
  title   = {Some new results on certain types of proximinality in Banach spaces},
  journal = {Adv. Inequal. Appl.},
  volume  = {2018},
  year    = {2018},
  pages   = {9},
  doi     = {10.28919/aia/3649}
}