The efficiency of approximating real numbers by Lüroth expansion

Chunyun Cao; Jun Wu; Zhenliang Zhang

Displaying similar documents to “The efficiency of approximating real numbers by Lüroth expansion”

The fractional dimensional theory in Lüroth expansion

Luming Shen, Kui Fang (2011)

Czechoslovak Mathematical Journal

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It is well known that every $x \in (0, 1]$ can be expanded to an infinite Lüroth series in the form of $x = \frac{1}{d_{1} (x)} + \dots + \frac{1}{d_{1} (x) (d_{1} (x) - 1) \dots d_{n - 1} (x) (d_{n - 1} (x) - 1) d_{n} (x)} + \dots,$ where $d_{n} (x) \geq 2$ for all $n \geq 1$ . In this paper, sets of points with some restrictions on the digits in Lüroth series expansions are considered. Mainly, the Hausdorff dimensions of the Cantor sets $F_{φ} = {x \in (0, 1] : d_{n} (x) \geq φ (n), \forall n \geq 1}$ are completely determined, where $φ$ is an integer-valued function defined on $ℕ$ , and $φ (n) \to \infty$ as $n \to \infty$ .

On the concept of optimality interval.

Bibiloni, Lluís, Viader, Pelegrí, Paradís, Jaume (2002)

International Journal of Mathematics and Mathematical Sciences

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King type modification of $q$ -Bernstein-Schurer operators

Mei-Ying Ren, Xiao-Ming Zeng (2013)

Czechoslovak Mathematical Journal

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Very recently the $q$ -Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve $x^{2}$ (2003), in this paper we modify $q$ -Bernstein-Schurer operators to King type modification of $q$ -Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions $x^{2}$ and study the approximation properties of these operators. We establish a convergence...

Continued fractions and the Gauss map.

Bates, Bruce, Bunder, Martin, Tognetti, Keith (2005)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Mittag-Leffler type expansions of $\bar{\partial}$ -closed $(0, n - 1)$ -forms in certain domains in $ℂ^{n}$

Telemachos Hatziafratis (2003)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we will prove a Mittag-Leffler type theorem for $\bar{\partial}$ -closed $(0, n - 1)$ -forms in $ℂ^{n}$ by addressing the question of constructing such differential forms with prescribed periods in certain domains.

Displaying similar documents to “The efficiency of approximating real numbers by Lüroth expansion”

The fractional dimensional theory in Lüroth expansion

On the concept of optimality interval.

King type modification of q -Bernstein-Schurer operators

Continued fractions and the Gauss map.

Mittag-Leffler type expansions of ∂ ¯ -closed ( 0 , n - 1 ) -forms in certain domains in ℂ n

King type modification of $q$ -Bernstein-Schurer operators

Mittag-Leffler type expansions of $\bar{\partial}$ -closed $(0, n - 1)$ -forms in certain domains in $ℂ^{n}$