On Some Approximation Properties for a Sequence of λ-Bernstein Type Operators
Keyword(s):
In 2010, Long and Zeng introduced a new generalization of the Bernstein polynomials that depends on a parameter and called -Bernstein polynomials. After that, in 2018, Lain and Zhou studied the uniform convergence for these -polynomials and obtained a Voronovaskaja-type asymptotic formula in ordinary approximation. This paper studies the convergence theorem and gives two Voronovaskaja-type asymptotic formulas of the sequence of -Bernstein polynomials in both ordinary and simultaneous approximations. For this purpose, we discuss the possibility of finding the recurrence relations of the -th order moment for these polynomials and evaluate the values of -Bernstein for the functions , is a non-negative integer
2011 ◽
Vol 48
(1)
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pp. 23-43
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2013 ◽
Vol 50
(4)
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pp. 393-405
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Keyword(s):
2021 ◽
Vol 2
(2)
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pp. 38-49