Year: 2011
Analysis in Theory and Applications, Vol. 27 (2011), Iss. 1 : pp. 40–50
Abstract
In this paper we introduce a generalization of Bernstein polynomials based on $q$ calculus. With the help of Bohman-Korovkin type theorem, we obtain $A$−statistical approximation properties of these operators. Also, by using the Modulus of continuity and Lipschitz class, the statistical rate of convergence is established. We also gives the rate of $A$−statistical convergence by means of Peetre’s type $K$−functional. At last, approximation properties of a rth order generalization of these operators is discussed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.1007/s10496-011-0040-8
Analysis in Theory and Applications, Vol. 27 (2011), Iss. 1 : pp. 40–50
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: $q$−integers $q$−Bernstein polynomials $A$−statistical convergence modulus of continuity Lipschitz class Peetre’s type $K$−functional.