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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 8, pp. 1106–1116, August, 2014.
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Kuchmins’ka, K.Y. Boundary Versions of the Worpitzky Theorem for Two-Dimensional Continued Fractions. Ukr Math J 66, 1236–1247 (2015). https://doi.org/10.1007/s11253-015-1005-4
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DOI: https://doi.org/10.1007/s11253-015-1005-4