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

TL;DR

This paper investigates the convergence criteria of sequences based on positive and alternating Perron expansions, which are essential for understanding the continuity of functions defined through these representations.

Contribution

It introduces new conditions for sequence convergence in terms of Perron expansions, impacting the analysis of function continuity.

Findings

Established convergence conditions for sequences with Perron expansions

Linked Perron representations to function continuity criteria

Provided theoretical foundations for further analysis of Perron-based functions

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.