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Eurasian Mathematical Journal, 2014, том 5, номер 3, страницы 46–57
(Mi emj163)
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Rate of approximation by modified Gamma-Taylor operators
A. Izgi Department of Mathematics, Harran University, Science and Arts Faculty, Osmanbey Kampüsü, 63300-Ş.Urfa / Turkey
Аннотация:
In this paper we consider the following modification of the Gamma operators which were first introduced in [8] (see [17], [18] and [8] respectively)
$$
A_n(f; x)=\int_0^\infty K_n(x, t)f(t)dt
$$
where
$$
K_n(x, t)=\frac{(2n+3)!}{n!(n+2)!}\frac{t^nx^{n+3}}{(x+t)^{2n+4}}, \quad x, t\in(0, \infty),
$$
and the following modified Gamma-Taylor operators
$$
A_{n,r}(f;x)=\int_0^\infty K_n(x, t)\left(\sum_{i=0}^r\frac{f^{(i)}(t)}{i!}(x-t)^i\right)dt.
$$
We establish some approximation properties of these operators. At the end of the
paper we also present some graphs allowing to compare the rate of approximation of $f$ by $A_n(f; x)$ and $A_{n,r}(f; x)$ for certain $n$, $r$ and $x$.
Ключевые слова и фразы:
approximation, Gamma operators, modulus of continuity in weighted spaces, linear positive operators, Taylor polynomials.
Поступила в редакцию: 31.08.2012
Образец цитирования:
A. Izgi, “Rate of approximation by modified Gamma-Taylor operators”, Eurasian Math. J., 5:3 (2014), 46–57
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj163 https://www.mathnet.ru/rus/emj/v5/i3/p46
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Страница аннотации: | 230 | PDF полного текста: | 148 | Список литературы: | 34 |
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