Abstract
In the present paper, we find that the Bernstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallée properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Berens, H. and Xu, Y., On Bernstein-Durrmeyer Polynomials with Jacobi-weights, In: Approximation Theory and Functional Analysis Conference, C. K. Chui(ed), Academic Press, Boston, (1991), 25–46.
Berens, H. and Xu, Y., On Bernstein-Durrmeyer Polynomials with Jacobi-weights: The Case p = 1 and p = +∞, In: Approximation Interpolation and Summability, Israel Mathematical Conference Proceedings, S, Baron, D. Leviatan(ed), Weizmann Science Press of Israel, Israel, (1991), 51–62.
Szegö, G., Orthogonal Polynomials, Amer. Math. Soc. Collog. Publ., 1976, 23.
Askey, R. and Wainger, S., A Convolution Structure for Jacobi Series, Amer. J. Math., 91(1969), 463–485.
Nevai, P.G., Orthogonal Polynomials, AMS, 18(213)(1979),167–168.
Ivanov, V.I., Some Extremal Properties of Polynomials and Inverse Inequalities of Approximation, Proceeding of the Steklov Institute of Mathematics, (1)(1981), 85–120.
Chen, W., Ditzian, Z. and Ivanov, K., Strong Converse Inequality for the Bernstein-Durrmeyer Operator, J. Approx. Theory, 75(1)(1993), 25–43.
Pawelke, V. S., Ein satz vom Jacksonschen typ für Algebraische Polynome, Acta Sci. Math.(Szeged), 33(1972), 323–336.
Author information
Authors and Affiliations
Additional information
Supported by the NSF of P.R.China(10471130), and the NSF of Zhejiang Province(Y604003).
Rights and permissions
About this article
Cite this article
Sheng, B., Zhang, C. An application of Bernstein-Durrmeyer operators. Analys in Theo Applic 23, 16–25 (2007). https://doi.org/10.1007/s10496-001-0016-1
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10496-001-0016-1