On global smoothness preservation by Bernstein-type operators
Keywords:
Global smoothness preservation, second order modulus of continuity, simultaneous approximation, Bernstein-type operators.Abstract
We study global smoothness preservation of a function f by sequences of Bernstein-type operators with respect to a certain modulus of continuity of order two.
Mathematics Subject Classification (2010): 41A36, 41A17.
References
Adell, J.A., de la Cal, J., Preservation of moduli of continuity by Bernstein-type operators, in Approximation, Probability and Related Fields (G.A. Anastassiou and S.T. Rachev Eds.), Plenum Press, New York, (1994), 1-18.
Anastassiou, G.A., Cottin, C., Gonska, H.H., Global smoothness of approximating functions, Analysis, Munich, 11(1991), 43-57.
Anastassiou, G.A., Gal, S., Approximation Theory: Moduli of Continuity and Global Smoothness Preservation, Birkhauser, Boston, 2000.
Brown, B.M., Elliot, D., Paget, D.F., Lipschitz constants for the Bernstein polynomials of a Lipschitz continuous function, J. Approx. Theory, 49(1987), 196-199.
Cottin, C., Gonska, H.H., Simultaneous approximation and global smoothness preservation, Rend. Circ. Mat. Palermo (2) Suppl., 33(1993), 259-279.
Hajek, D., Uniform polynomial approximation, Amer. Math. Monthly, 72(1965), 681.
Lindvall, T., Bernstein polynomials and the law of large numbers, Math. Scientist, 7(1982), 127-139.
Paltanea, R., Improved constant in approximation with Bernstein operators, Research Semin. Fac. Math. Babes-Bolyai Univ. 6, Univ. Babes-Bolyai, Cluj-Napoca, (1988), 261-268.
Paltanea, R., Approximation theory using positive linear operators, Birkhauser, 2004.
Zhou, D.-X., On a problem of Gonska, Results Math., 28(1995), 169-183.
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