Approximation by q -Bernstein Polynomials in the Case q → 1 +
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-11
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
Let B n , q ( f ; x ) , q ∈ ( 0 , ∞ ) be the q -Bernstein polynomials of a function f ∈ C [ 0,1 ] .
It has been known that, in general, the sequence B n , q n ( f ) with q n → 1 + is not an approximating sequence for f ∈ C [ 0,1 ] , in contrast to the standard case q n → 1 - .
In this paper, we give the sufficient and necessary condition under which the sequence B n , q n ( f ) approximates f for any f ∈ C [ 0,1 ] in the case q n > 1 .
Based on this condition, we get that if 1 < q n < 1 + ln 2 / n for sufficiently large n , then B n , q n ( f ) approximates f for any f ∈ C [ 0,1 ] .
On the other hand, if B n , q n ( f ) can approximate f for any f ∈ C [ 0,1 ] in the case q n > 1 , then the sequence ( q n ) satisfies lim ¯ n → ∞ n ( q n - 1 ) ≤ ln 2 .
American Psychological Association (APA)
Wu, Xuezhi. 2014. Approximation by q -Bernstein Polynomials in the Case q → 1 +. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-1013572
Modern Language Association (MLA)
Wu, Xuezhi. Approximation by q -Bernstein Polynomials in the Case q → 1 +. Abstract and Applied Analysis No. 2014 (2014), pp.1-6.
https://search.emarefa.net/detail/BIM-1013572
American Medical Association (AMA)
Wu, Xuezhi. Approximation by q -Bernstein Polynomials in the Case q → 1 +. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-1013572
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013572