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A Study on -Quasi-Cauchy Sequences

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  • Hüseyin Çakalli
  • Huseyin Kaplan

Abstract

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

Suggested Citation

  • Hüseyin Çakalli & Huseyin Kaplan, 2013. "A Study on -Quasi-Cauchy Sequences," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-4, March.
    • Handle: RePEc:hin:jnlaaa:836970
    DOI: 10.1155/2013/836970
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