The Arzelà-Ascoli theorem by means of ideal convergence


Taş E., YURDAKADİM T.

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.