Estimation of the Rates of Pointwise and Uniform Convergence of Branched Continued Fractions with Inequivalent Variables

Abstract

We study branched continued fractions with inequivalent variables, branched continued fractions of the special form, and multidimensional C - and S -fractions with inequivalent variables. By using the results established for continued fractions and the results concerning the convergence and estimation of the errors of approximation of branched continued fractions of a special form in angular domains, we obtain new estimates for the rate of convergence of branched continued fractions of a special form, pointwise convergence of multidimensional C -fractions, and uniform convergence on compact sets of angular domains of multidimensional S -fractions with inequivalent variables.