Characterization of best uniform approximation with restricted ranges of derivatives

  • Xu Shusheng


This paper gives a general characterization theorem of a best uniform approximation of generalized polynomial having multiple restricted ranges of its derivatives. This theorem is widely applicable. The results on characterization in many standard approximations, such as approximation with Hermite-Birkhoff interpolatory side conditions, multiple comonotone approximation, and approximation by algebraic polynomials having bounded coefficients, etc., are special cases of our results.


Uniform Approximation Restrict Range Normed Linear Space Side Condition Algebraic Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Taylor, G.D., Approximation by Functions Having Restricted Ranges, III, Journal of Mathematical Analysis and Applications, 27(1969), 241–248.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    —, Approximation by Functions Having Restricted Ranges: Equality Case, Numer. Math., 14 (1969), 71–78.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Sippel, W., Approximation by Functions with Restricted Ranges, In: Lorentz, G.G. (ed.): Approximation Theory, New York: Academic Press, Inc. (1973), 481–484.Google Scholar
  4. [4]
    Shih, Y. K., Best Approximation Having Restricted Ranges with Nodes (Chinese), Journal of Computational Mathematics, 2(1980), 124–132.MATHGoogle Scholar
  5. [5]
    Xu, S.S., A Characterization of Best Approximations with Restricted Ranges, Journal of Approximation Theory, 71(1992), 193–212.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Kimchi, E. and Richter-Dyn, N., Best Uniform Approximation with Hertmite-Birkhoff Interpolatory Side Conditions, Journal of Approximation Theory, 15(1975), 85–100.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    —, Properties of Best Approximation with Interpolatory and Restricted Range Side Conditions, Journal of Approximation Theory, 15(1975), 101–115.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Lorentz, G. G. and Zeller, K. L., Monotone Approximation by Algebraic Polynomials, Transactions of the American Mathematical Society, 149(1970), 1–18.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Xu, S. S., Characterization Theorem of Generalized Polynomial of Best Approximation Having Bounded Coefficients, Acta Mathematicae Applicatae Sinica (English Ser.), 5(1989), 361–366.MATHCrossRefGoogle Scholar
  10. [10]
    Laurent, P. J., Approximation et Optimisation, Collection Enseignement des Science, No. 13, Hermann, Paris, 1972.MATHGoogle Scholar
  11. [11]
    Karlin, S. J., & Studden, W. J., Tchebycheff Systems: with Applications in Analysis and Statistics, Interscience Publications, New York, 1966.MATHGoogle Scholar

Copyright information

© Springer 1997

Authors and Affiliations

  • Xu Shusheng
    • 1
  1. 1.Department of mathematicsJiangnan UniversityWeuxi, Jiangsu ProvincePRC

Personalised recommendations