Abstract
In this paper it is proved that the class B of functions β with which the convolution operators Uρ are constructed contains elements such that if f belongs to a certain class M and if f″ (x) exists the rate of approximation of f(x) by (Uρ f)(x) (ρ → ∞) is very small.
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References
Sikkema, P.C., Estimations involving a modulus of continuity for a generalization of Korovkin’s operators. Linear Spaces and Approximation, eds. P.L. Butzer and B.Sz. -Nagy. (ISNM, vol. 40) Birkhäuser Verlag, Basel/Stuttgart 1978, 289–303.
Sikkema, P.C., Approximation formulae of Voronovskaya — type for certain convolution operators. J. Approximation Theory 26 (1979), 26–45.
Sikkema, P.C., Voronovskaya type formulae for convolution operators approximating with great speed. Approximation Theory III. Proc. Conf. on Approximation Theory, Austin (Tex.) U.S.A., 8–12 Jan. 1980.
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© 1981 Birkhäuser Verlag Basel
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Sikkema, P.C. (1981). Slow Approximation with Convolution Operators. In: Butzer, P.L., Sz.-Nagy, B., Görlich, E. (eds) Functional Analysis and Approximation. ISNM 60: International Series of Numerical Mathematics / ISNM 60: Internationale Schriftenreihe zur Numerischen Mathematik / ISNM 60: Série internationale d’Analyse numérique, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9369-5_29
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DOI: https://doi.org/10.1007/978-3-0348-9369-5_29
Publisher Name: Birkhäuser Basel
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