The Arzelà-Ascoli theorem by means of ideal convergence
Georgian Mathematical Journal, vol.25, no.3, pp.475-479, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 25 Issue: 3
- Publication Date: 2018
- Doi Number: 10.1515/gmj-2017-0052
- Journal Name: Georgian Mathematical Journal
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.475-479
- Keywords: classical Arzelà-Ascoli theorem, ideal convergence, Pointwise and uniform convergence
- Bilecik Şeyh Edebali University Affiliated: No
Abstract
In this paper, using the concept of ideal convergence, which extends the idea of ordinary convergence and statistical convergence, we are concerned with the I-uniform convergence and the I-pointwise convergence of sequences of functions defined on a set of real numbers D. We present the Arzelà-Ascoli theorem by means of ideal convergence and also the relationship between I-equicontinuity and I-continuity for a family of functions.