The convergence of sequences in terms of positive and alternating Perron expansions

Abstract

We consider conditions for the convergence of sequences in terms of positive and alternating Perron expansions ($P$-representation and $P^{-}$-representation). These conditions are crucial to determine the continuity of functions that are defined using $P$-representation or $P^{-}$-representation of real numbers.

10 pages, 5 figures