Characterization of absolute and uniform continuity


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ASLAN İ., DUMAN O.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.49, no.5, pp.1550-1565, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 5
  • Publication Date: 2020
  • Doi Number: 10.15672/hujms.585581
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1550-1565
  • Keywords: summability process, absolute continuity, uniform continuity, nonlinear integral operators, bounded variation, CONVERGENCE, SUMMABILITY
  • Hacettepe University Affiliated: Yes

Abstract

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.