2019
Том 71
№ 4

All Issues

Kuchmins’ka Kh. Yo.

Articles: 2
Article (Ukrainian)

Boundary Versions of the Worpitzky Theorem for Two-Dimensional Continued Fractions

Kuchmins’ka Kh. Yo.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 8. - pp. 1106–1116

For a two-dimensional continued fraction another generalization of the Worpitzky theorem is proved and the limit sets are proposed for Worpitzky-like theorems in the case where the element sets of the twodimensional continued fraction are replaced by their boundaries.

Article (Ukrainian)

Approximation Properties of Two-Dimensional Continued Fractions

Kuchmins’ka Kh. Yo., Sus' О. M., Vozna S. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 30-44

By using the difference formula for approximations of two-dimensional continued fractions, the method of fundamental inequalities, the Stieltjes–Vitali theorem, and generalizations of divided and inverse differences, we estimate the accuracy of approximations of two-dimensional continued fractions with complex elements by their convergents and obtain estimates for the real and imaginary parts of remainders of two-dimensional continued fractions. We also prove an analog of the van Vleck theorem and construct an interpolation formula of the Newton–Thiele type.