Acta Mathematica Hungarica

, Volume 52, Issue 1–2, pp 83–90 | Cite as

The prevalence of strong uniqueness inL1

  • J. R. Angelos
  • D. Schmidt
Article
  • 16 Downloads

Keywords

Strong Uniqueness 

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References

  1. [1]
    J. Angelos and A. Egger, Strong uniqueness in theL p spaces,J. Approx. Theory,42 (1984), 14–26.Google Scholar
  2. [2]
    J. Angelos and A. Kroó, The equivalence of the moduli of continuity of the best approximation operator and of strong unicity inL 1,J. Approx. Theory,46 (1986), 129–136.Google Scholar
  3. [3]
    I. Barrodale, M. J. D. Powell and F. D. K. Roberts, The differential correction algorithm for rationall approximation,SIAM J. Numer. Anal.,9 (1972), 493–504.Google Scholar
  4. [4]
    E. W. Cheney and D. E. Wulbert, The existence and uniqueness of best approximations,Math. Scand.,24 (1969), 113–140.Google Scholar
  5. [5]
    L. Cromme, Strong uniqueness, a far reaching criterion for convergence analysis of iterative processes,Numer. Math.,29 (1978), 179–193.Google Scholar
  6. [6]
    A. L. Garkavi, On Cebysev and almost Cebysev subspaces,Amer. Math. Soc. Transl.,96 (1970), 177–187.Google Scholar
  7. [7]
    A. Kroó, On the continuity of best approximations in the space of integrable functions,Acta Math. Acad. Sci. Hung.,32 (1978), 331–348.Google Scholar
  8. [8]
    A. Kroó, BestL 1-approximation on finite point sets: rate of convergence,J. Approx. Theory,33 (1981), 340–352.Google Scholar
  9. [9]
    D. J. Newman and H. S. Shapiro, Some theorems on Čebyŝev approximation,Duke Math. J.,30 (1963), 673–681.Google Scholar
  10. [10]
    G. Nürnberger, Unicity and strong unicity in approximation theory,J. Approx. Theory,22 (1979), 54–70.Google Scholar
  11. [11]
    G. Nürnberger and I. Singer, Uniqueness and strong uniqueness of best approximations by spline subspaces and other subspaces,J. Math. Anal. Applic.,90 (1982), 171–184.Google Scholar
  12. [12]
    R. R. Phelps, Cebysev subspaces of finite dimension inL 1,Proc. of the Amer. Math. Soc.,17 (1966), 646–652.Google Scholar
  13. [13]
    E. Rozema, Almost Chebyshev subspaces ofL 1(μ,E),Pacific J. Math.,53 (1974), 585–603.Google Scholar
  14. [14]
    I. Singer,The Theory of Best Approximation and Functions Analysis, SIAM (Philadelphia, 1974).Google Scholar
  15. [15]
    D. E. Wulbert, Uniqueness and differential characterization of approximation from manifolds of functions,Amer. J. Math.,18 (1971), 350–366.Google Scholar

Copyright information

© Akadémiai Kiadó 1988

Authors and Affiliations

  • J. R. Angelos
    • 1
  • D. Schmidt
    • 2
  1. 1.Department of MathematicsCentral Michigan UniversityMt. PleasantUSA
  2. 2.Department of Mathematical SciencesOakland UniversityRochesterUSA

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