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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.
-
Operators, Inequalities and Approximation
Approximation by a Double Sequence of Operators Involving Multivariable q-Lagrange–Hermite Polynomials
Baxhaku, Behar | Agrawal, Purshottam Narain | Lachhwani, Kailash Chandra2024
https://doi.org/10.1007/978-981-97-3238-8_1 [Citations: 0] -
A certain family of mixed summation-integral-type Lupaş-Phillips-Bernstein operators
Sharma, Honey | Aujla, Jaspal SinghMathematical Sciences, Vol. 6 (2012), Iss. 1 P.26
https://doi.org/10.1186/2251-7456-6-26 [Citations: 2] -
A q‐Erkuş–Srivastava polynomials operator
Agrawal, Purshottam Narain | Baxhaku, Behar | Singh, Jitendra KumarMathematical Methods in the Applied Sciences, Vol. 47 (2024), Iss. 8 P.7079
https://doi.org/10.1002/mma.9958 [Citations: 2]