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The element sets and value sets of two-dimensional continued fractions

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Abstract

For two-dimensional continued fractions we prove the existence and uniqueness of an optimal sequence of value sets corresponding to an arbitrarily given sequence of element sets. We compute the element set for a given sequence of disk value sets and as a corollary, give the element sets and value sets that are used in convergence criteria for two-dimensional continued fractions.

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Authors
  1. Kh. I. Kuchmins'ka
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Additional information

Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 55–61.

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Kuchmins'ka, K.I. The element sets and value sets of two-dimensional continued fractions. J Math Sci 90, 2368–2373 (1998). https://doi.org/10.1007/BF02433968

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  • DOI: https://doi.org/10.1007/BF02433968

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