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Higher order limit q ‐Bernstein operators
Author(s) -
Mahmudov N. I.
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1469
Subject(s) - mathematics , bernstein polynomial , limit (mathematics) , baskakov operator , generalization , order (exchange) , operator theory , moment (physics) , pure mathematics , spectral theorem , microlocal analysis , mathematical analysis , fourier integral operator , algebra over a field , quantum mechanics , physics , finance , economics
In this paper we give the estimates of the central moments for the limit q ‐Bernstein operators. We introduce the higher order generalization of the limit q ‐Bernstein operators and using the moment estimations study the approximation properties of these newly defined operators. It is shown that the higher order limit q ‐Bernstein operators faster than the q ‐Bernstein operators for the smooth functions defined on [0, 1]. Copyright © 2011 John Wiley & Sons, Ltd.