Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON ω-CHEBYSHEV SUBSPACES IN BANACH SPACES

  • Published : 2008.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this paper is to introduce and discuss the concept of ${\omega}$-Chebyshev subspaces in Banach spaces. The concept of quasi Chebyshev in Banach space is defined. We show that ${\omega}$-Chebyshevity of subspaces are a new class in approximation theory. In this paper, also we consider orthogonality in normed spaces.

Keywords

References

  1. D. Narayana and T. S. S. R. K. Rao, Some remarks on quasi-Chebyshev subspaces, J. Math. Anal. Appl. 321 (2006), no. 1, 193-197 https://doi.org/10.1016/j.jmaa.2005.08.027
  2. C. Franchetti and M. Furi, Some characteristic properties of real Hilbert spaces, Rev. Roumaine Math. Pures. Appl. 17 (1972), 1045-1048
  3. H. Mazaheri and F. M. Maalek Ghaini, Quasi-orthogonality of the best approximant sets, Nonlinear Anal. 65 (2006), no. 3, 534-537 https://doi.org/10.1016/j.na.2005.09.026
  4. H. Mazaheri and S. M. Vaezpour, Orthogonality and $\epsilon$-orthogonality in Banach spaces, Aust. J. Math. ASnal. Appl. 2 (2005) no. 1, Art. 10, 1-5
  5. P. L. Papini and I. Singer, Best coapproximation in normed linear spaces, Monatsh. Math. 88 (1979), no. 1, 27-44 https://doi.org/10.1007/BF01305855
  6. I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, New York-Berlin, 1970

Cited by

  1. On simultaneous weakly-Chebyshev subspaces vol.27, pp.2, 2011, https://doi.org/10.1007/s10496-011-0117-4