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A Study on Nθ‐Quasi‐Cauchy Sequences

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  • Hüseyin Çakalli
  • Huseyin Kaplan

Abstract

Recently, the concept of Nθ‐ward continuity was introduced and studied. In this paper, we prove that the uniform limit of Nθ‐ward continuous functions is Nθ‐ward continuous, and the set of all Nθ‐ward continuous functions is a closed subset of the set of all continuous functions. We also obtain that a real function f defined on an interval E is uniformly continuous if and only if (f(αk)) is Nθ‐quasi‐Cauchy whenever (αk) is a quasi‐Cauchy sequence of points in E.

Suggested Citation

  • Hüseyin Çakalli & Huseyin Kaplan, 2013. "A Study on Nθ‐Quasi‐Cauchy Sequences," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:836970
    DOI: 10.1155/2013/836970
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    References listed on IDEAS

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    1. H. Çakalli, 2008. "Slowly Oscillating Continuity," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
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