An analog of the Vorpits'kii convergence criterion for branched continued fractions of special form

Abstract

We study branched continued fractions of a special form with inequivalent variables. We establish a multidimensional analog of the Vorpits 'kii convergence criterion for continued fractions.

On the convergence of branched continued fractions

“…were studied in [4,23]. Another peculiarity of the special constructions proposed above for branched continued fractions is the choice of their approximants.…”

A Worpitzky boundary theorem for branched continued fractions of the special form

“…Since the beginning we prove the Worpitsky-like theorem in a slightly more general form than it was done in [1].…”

“…For the difference between the nth and mth approximants of the BCF of the special form (8) the following relation is true [1]:…”

Оцінки Швидкості Збіжності 1-Періодичного Гіллястого Ланцюгового Дробу Спеціального Вигляду

“…Баран [5] довела збiжнiсть та встановила оцiнку швидкостi збiжностi дробу (4), якщо всi його елементи задовольняють умови [2,3,4] Т. Антонова дослiдила круговi та параболiчнi областi збiжностi дробу (4) та встановила оцiнки швидкостi збiжностi при певних додаткових умовах на елементи цього дробу.…”