Displaying similar documents to “The fractional dimensional theory in Lüroth expansion”

The efficiency of approximating real numbers by Lüroth expansion

Chunyun Cao, Jun Wu, Zhenliang Zhang (2013)

Czechoslovak Mathematical Journal

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For any x ∈ ( 0 , 1 ] , let x = 1 d 1 + 1 d 1 ( d 1 - 1 ) d 2 + ⋯ + 1 d 1 ( d 1 - 1 ) ⋯ d n - 1 ( d n - 1 - 1 ) d n + ⋯ be its Lüroth expansion. Denote by P n ( x ) / Q n ( x ) the partial sum of the first n terms in the above series and call it the n th convergent of x in the Lüroth expansion. This paper is concerned with the efficiency of approximating real numbers by their convergents { P n ( x ) / Q n ( x ) } n ≥ 1 in the Lüroth expansion. It is shown that almost no points can have convergents as the optimal approximation for infinitely many times in the Lüroth expansion. Consequently, Hausdorff dimension is introduced to quantify...

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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