Characterization of absolute and uniform continuity

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ASLAN İ., DUMAN O.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.49, sa.5, ss.1550-1565, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 5
  • Basım Tarihi: 2020
  • Doi Numarası: 10.15672/hujms.585581
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1550-1565
  • Anahtar Kelimeler: summability process, absolute continuity, uniform continuity, nonlinear integral operators, bounded variation, CONVERGENCE, SUMMABILITY
  • Hacettepe Üniversitesi Adresli: Evet

Özet

In the present paper, by considering nonlinear integral operators and using their approximations via regular summability methods, we obtain characterizations for some function spaces including the space of absolutely continuous functions, the space of uniformly continuous functions, and their other variants. We observe that Bell-type summability methods are quite effective to generalize and improve some related results in the literature. At the end of the paper, we discuss some special cases and applications.