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2016 | 70 | 1 |
Tytuł artykułu

On strong proximinality in normed linear spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
70
Numer
1
Opis fizyczny
Daty
wydano
2016
online
2016-07-04
Twórcy
Bibliografia
  • Bandyopadhyay, Pradipta, Li, Yongjin, Lin, Bor-Luh, Narayana, Darapaneni, Proximinality in Banach spaces, J. Math. Anal. Appl. 341 (2008), 309-317.
  • Cheney, E. W., Wulbert, D. E., The existence and uniqueness of best approximation, Math. Scand. 24 (1969), 113-140.
  • Dutta, S., Shunmugraj, P., Strong proximinality of closed convex sets, J. Approx. Theory 163 (2011), 547-553.
  • Effimov, N. V., Steckin, S. B., Approximative compactness and Chebyshev sets, Soviet Math. Dokl. 2 (1961), 1226-1228.
  • Finet, C., Quarta, L., Some remarks on M-ideals and strong proximinality, Bull. Korean Math. Soc. 40 (2003), 503-508.
  • Godefroy, G., Indumathi, V., Strong proximinality and polyhedral spaces, Rev. Mat. Complut. 14 (2001), 105-125.
  • Jayanarayanan, C. R., Paul, T., Strong proximinality and intersection properties of balls in Banach spaces, J. Math. Anal. Appl. 426 (2015), 1217-1231.
  • Narayana, D., Strong proximinality and renorming, Proc. Amer. Math. Soc. 134 (2005), 1167-1172.
  • Panda, B. B., Kapoor, O. P., A generalization of the local uniform rotundity of the norm, J. Math. Anal. Appl. 52 (1975), 300-308.
  • Singer, I., Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, New York, 1967.
  • Vlasov, L. P., The concept of approximative compactness and its variants, Mat. Zametki 16 (1974), 337-348 (Russian), English transl. in Math. Notes 16, No. 2 (1974), 786-792.
  • Zhang, Z. H., Shi, Z. R., Convexities and approximative compactness and continuity of metric projection in Banach spaces, J. Approx. Theory 161 (2009), 802-812.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2016_70_1_19
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