Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Best possible approximation constants


Author: A. M. Fink
Journal: Trans. Amer. Math. Soc. 226 (1977), 243-255
MSC: Primary 41A50
DOI: https://doi.org/10.1090/S0002-9947-1977-0447915-8
MathSciNet review: 0447915
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study inequalities between the norm of the best approximating polynomial and the nth derivative of the function. These inequalities are then related to inequalities that have been considered elsewhere in different contexts.


References [Enhancements On Off] (What's this?)

  • [1] G. M. Phillips, Error estimates for best polynomial approximations, Approximation Theory (Proc. Sympos., Lancaster, 1969), Academic Press, London, 1970, pp. 1-6. MR 43 #3703. MR 0277970 (43:3703)
  • [2] A. M. Fink, Conjugate inequalities for functions and their derivatives, SIAM J. Math. Anal. 5 (1974), 399-411. MR 49 #7407. MR 0342662 (49:7407)
  • [3] -, Differential inequalities and disconjugacy, J. Math. Anal. Appl. 49 (1975), 758-772. MR 0379958 (52:862)
  • [4] J. Brink, Inequalities involving $ {\left\Vert f \right\Vert _p}$ and $ {\left\Vert {{f^{(n)}}} \right\Vert _q}$ for f with n zeros, Pacific J. Math. 42 (1972), 289-311. MR 0315069 (47:3618)
  • [5] G. Meinardus, Approximation of functions. Springer, Berlin, 1964; English transl., Springer-Verlag, New York, 1967. MR 31 #547; 36 #571.
  • [6] G. G. Lorentz, Approximation of functions, Holt, Rinehart and Winston, New York, 1966. MR 35 #4642; erratum, 36, p. 1567. MR 0213785 (35:4642)
  • [7] I. J. Schoenberg, The perfect B-splines and a time-optional control problem, Israel J. Math. 10 (1971), 261-274. MR 47 #9130. MR 0320594 (47:9130)
  • [8] M. A. Krasnosel'skiĭ, Positive solutions of operator equations, Fizmatgiz, Moscow, 1962; English transl. Noordhoff, Groningen, 1964. MR 26 #2862; 31 #6107. MR 0181881 (31:6107)
  • [9] I. J. Schoenberg, Cardinal spline interpolation, SIAM Regional Conf. Ser. Appl. Math., no. 12, 1973. MR 0420078 (54:8095)
  • [10] J. Brink, Private communication.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 41A50

Retrieve articles in all journals with MSC: 41A50


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0447915-8
Keywords: Best polynomial approximation
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society