The Arzelà-Ascoli theorem by means of ideal convergence

Taş E., YURDAKADİM T.

Georgian Mathematical Journal, cilt.25, sa.3, ss.475-479, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1515/gmj-2017-0052
  • Dergi Adı: Georgian Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.475-479
  • Anahtar Kelimeler: classical Arzelà-Ascoli theorem, ideal convergence, Pointwise and uniform convergence
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

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.