Abstract and Applied Analysis
Volume 2013 (2013), Article ID 836970, 4 pages
http://dx.doi.org/10.1155/2013/836970
Research Article

A Study on -Quasi-Cauchy Sequences

Hüseyin Çakalli1 and Huseyin Kaplan2

1Maltepe University, Department of Mathematics, Faculty of Arts and Science, Marmara Eğitim Köyü, Maltepe, 34857 Istanbul, Turkey
2Department of Mathematics, Niğde University, Faculty of Science and Letters, 051100 Niğde, Turkey

Received 14 November 2012; Revised 24 January 2013; Accepted 15 February 2013

Academic Editor: Ziemowit Popowicz

Copyright © 2013 Hüseyin Çakalli and Huseyin Kaplan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 .