Uniform separation through intermediate points

TL;DR

The paper proves that a separated sequence in the unit disc is uniformly separated if an intermediate sequence with certain properties exists, and applies this to enhance results in differential equations.

Contribution

It introduces a new criterion linking intermediate sequences to uniform separation, improving existing theorems in complex analysis and differential equations.

Findings

Separated sequences are uniformly separated under specific intermediate sequence conditions

The property enhances understanding of sequence separation in complex analysis

Application to improve results in differential equations

Abstract

It is shown that a separated sequence of points in the unit disc of the complex plane is in fact uniformly separated, if there exists a certain intermediate sequence whose separated subsequences are uniformly separated. This property is applied to improve a recent result in the theory of differential equations.