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2013 A Study on N θ -Quasi-Cauchy Sequences
Hüseyin Çakalli, Huseyin Kaplan
Abstr. Appl. Anal. 2013: 1-4 (2013). DOI: 10.1155/2013/836970

Abstract

Recently, the concept of N θ -ward continuity was introduced and studied. In this paper, we prove that the uniform limit of N θ -ward continuous functions is N θ -ward continuous, and the set of all N θ -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 ( α k )) is N θ -quasi-Cauchy whenever ( α k ) is a quasi-Cauchy sequence of points in E .

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Hüseyin Çakalli. Huseyin Kaplan. "A Study on N θ -Quasi-Cauchy Sequences." Abstr. Appl. Anal. 2013 1 - 4, 2013. https://doi.org/10.1155/2013/836970

Information

Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1276.26004
MathSciNet: MR3035304
Digital Object Identifier: 10.1155/2013/836970

Rights: Copyright © 2013 Hindawi

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