On Worpitzky-like theorems for a two-dimensional continued fraction

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.