The existence of polynomials of better approximation for continuous functions
DOI:
https://doi.org/10.5902/2179460X24873Abstract
The paper presents the problem of monotonic approximation which consists on finding a better polynomial approximation for a continuous real function "f" defined on [a, b]. (...). The existence of polynomials of better approximation for a given function "f" was presented here.
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References
CHENEY, E.W. Introduction to Approximate Theory. New York, McGraw-Hill Book Company, 1966.
LIMA, E.L. Espaços Métricos. Rio de Janeiro, Instituto de Matemática Pura e Aplicada, CNPq, 1977.
LORENTZ, G.G. Approximation of functions. New York, Rinehart and Winston, 1966.
LORENTZ, G.G. and ZELLER, K.L. Monotone approximation by algebraic polynomials. Trans. Amer. Math. Soc. 149: 1-18, 1970.
SHISHA, O. Monotone Approximation. Pacific J. Math. 15: 667-671, 1965.
LORENTZ, R.A. Uniquenes of Best Approximation by Monotone Polynomials. J. Approximation Theory 4:401-418, 1971.
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