TY - JOUR
T1 - Approximation Properties of rth Order Generalized Bernstein Polynomials Based on $q$-Calculus
AU - H. Sharma
JO - Analysis in Theory and Applications
VL - 1
SP - 40
EP - 50
PY - 2011
DA - 2011/01
SN - 27
DO - http://doi.org/10.1007/s10496-011-0040-8
UR - https://global-sci.org/intro/article_detail/ata/4578.html
KW - $q$−integers, $q$−Bernstein polynomials, $A$−statistical convergence, modulus of continuity, Lipschitz class, Peetre’s type $K$−functional.
AB - <p style="text-align: justify;">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.</p>