ON WORPITZKY-LIKE THEOREMS FOR A TWO-DIMENSIONAL CONTINUED FRACTION

Kh. Yo. Kuchminska

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ON WORPITZKY-LIKE THEOREMS FOR A TWO-DIMENSIONAL CONTINUED FRACTION

机译：二维连续分数的Wurpitzzky类定理

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Using estimates for the remainders of a two-dimensional continued fraction, the relation for the difference between two approximants of such a fraction in terms of these remainders, and the majorant method, we have proposed generalizations of the Worpitzky convergence theorem. For fractions satisfying the conditions of generalized Worpitzky theorems, we have also obtained estimates for their convergence rate.

机译：使用二维连续分数的余数的估计，根据这些余数的分数的两个近似值之间的差的关系以及主要方法，我们提出了Worpitzky收敛定理的推广。对于满足广义Worpitzky定理条件的分数，我们还获得了其收敛速度的估计值。

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来源
《Journal of Mathematical Sciences》 |2012年第1期|p.1-14|共14页
作者
Kh. Yo. Kuchminska;
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作者单位

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine;

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机译：Engel持续分数中部分和限制定理
5. Rates of convergence of continued fractions and an approximation theorem. [D] . Al-Fadhel, Tariq Abdulrahman. 2003

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6. A Gauss-Kuzmin Theorem for Continued Fractions Associated with Nonpositive Integer Powers of an Integer m ≥ 2 [O] . Dan Lascu -1

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7. A two-dimensional Gauss-Kuzmin theorem for singular continued fractions [O] . Ileana Sebe Gabriella 2000

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8. A Convergence Theorem for Noncommutative Continued Fractions [R] . Fair, W. 1970

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ON WORPITZKY-LIKE THEOREMS FOR A TWO-DIMENSIONAL CONTINUED FRACTION

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