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BEST COAPPROXIMATION IN L1 ;X

Yıl 2018, Cilt: 8 Sayı: 2, 448 - 453, 01.12.2018

Öz

Let X be a real Banach space and let G be a closed subset of X. The set G is called coproximinal in X if for each x ∈ X, there exists y0 ∈ G such that ky − y0k ≤ kx − yk , for all y ∈ G. In this paper, we study coproximinality of L ∞ µ, G in L ∞ µ, X , when G is either separable or reflexive coproximinal subspace of X.

Kaynakça

  • Diestel, J., Uhl J. R., (1997), Vector Measures, Math. Surveys Monograghs, Vol. 15, Amer. Math. Soc. Providence, RI.
  • Franchetti, C., Furi, M., (1972), Some Characteristic Properties of Real Hilbert Spaces, Rev. Roumaine Math. Pures Appl, 17, pp. 1045-1048.
  • Haddadi M. R., Hejazjpoor N., Mazaheri, H., (2010), Some Results About Best Coapproximation in Lp(S, X), Anal. Theory Appl., 26 (1), pp. 69-75.
  • Jawdat, J., Al-sharif Sh., (2016), Coproximinality Results in K¨othe Bochner Spaces, Italian J. of Pure and Applied Math., 36, pp. 783-790.
  • Kuratowski K., Ryll-Nardzewski C., (1965), A general theorem on selectors, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 13, pp. 397403.
  • Light W. and Cheney E., (1985), Approximation Theory in Tensor Product Spaces, Lecture Notes in Math. 1169, Springer, New York.
  • Lindenstrauss J., Tzafriri L., (1979), Classical Banach Spaces II, Function Spaces, Springer-Verlag, New York.
  • Mazaheri H., Jesmani S., (2007), Some results on best coapproximation in L1(I, G), Mediterr. J. Math., 26 (1), pp. 497-503.
  • Narang T. D., (1991), Best Coapproximation in Normed Linear Spaces, Rocky Mountain Journal of Mathematics, 22 (1), pp. 265-287.
  • Papini P. L., Singer I., (1979), Best Coapproximation in Normed Linear Spaces, Mh. Math., 88, pp. 27-44.
  • Rao, G. S., Chandrasekaran K. R., (1987), Characterizations of elements of best coapproximation in normed linear spaces, Pure and Applied Mathematika Sciences, 26, pp. 139-147.
  • Soni, D. C.; Bahadur, Lal, (1991), A Note on Coapproximation, Indian J. Pure Appl. Math., 22 (7), pp. 579- 582.
Yıl 2018, Cilt: 8 Sayı: 2, 448 - 453, 01.12.2018

Öz

Kaynakça

  • Diestel, J., Uhl J. R., (1997), Vector Measures, Math. Surveys Monograghs, Vol. 15, Amer. Math. Soc. Providence, RI.
  • Franchetti, C., Furi, M., (1972), Some Characteristic Properties of Real Hilbert Spaces, Rev. Roumaine Math. Pures Appl, 17, pp. 1045-1048.
  • Haddadi M. R., Hejazjpoor N., Mazaheri, H., (2010), Some Results About Best Coapproximation in Lp(S, X), Anal. Theory Appl., 26 (1), pp. 69-75.
  • Jawdat, J., Al-sharif Sh., (2016), Coproximinality Results in K¨othe Bochner Spaces, Italian J. of Pure and Applied Math., 36, pp. 783-790.
  • Kuratowski K., Ryll-Nardzewski C., (1965), A general theorem on selectors, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 13, pp. 397403.
  • Light W. and Cheney E., (1985), Approximation Theory in Tensor Product Spaces, Lecture Notes in Math. 1169, Springer, New York.
  • Lindenstrauss J., Tzafriri L., (1979), Classical Banach Spaces II, Function Spaces, Springer-Verlag, New York.
  • Mazaheri H., Jesmani S., (2007), Some results on best coapproximation in L1(I, G), Mediterr. J. Math., 26 (1), pp. 497-503.
  • Narang T. D., (1991), Best Coapproximation in Normed Linear Spaces, Rocky Mountain Journal of Mathematics, 22 (1), pp. 265-287.
  • Papini P. L., Singer I., (1979), Best Coapproximation in Normed Linear Spaces, Mh. Math., 88, pp. 27-44.
  • Rao, G. S., Chandrasekaran K. R., (1987), Characterizations of elements of best coapproximation in normed linear spaces, Pure and Applied Mathematika Sciences, 26, pp. 139-147.
  • Soni, D. C.; Bahadur, Lal, (1991), A Note on Coapproximation, Indian J. Pure Appl. Math., 22 (7), pp. 579- 582.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

J. Jawdat Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 8 Sayı: 2

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