Characterization of absolute and uniform continuity


ASLAN İ. , DUMAN O.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.49, ss.1550-1565, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 49 Konu: 5
  • Basım Tarihi: 2020
  • Doi Numarası: 10.15672/hujms.585581
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Sayfa Sayıları: ss.1550-1565

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.