Affiliation:
1. Department of Mathematics, Maltepe University, Marmara Education Village, 34857 Istanbul, Turkey
Abstract
A function is continuous if and only if preserves convergent sequences; that is, is a convergent sequence whenever is convergent. The concept of -ward continuity is defined in the sense that a function is -ward continuous if it preserves -quasi-Cauchy sequences; that is, is an -quasi-Cauchy sequence whenever is -quasi-Cauchy. A sequence of points in , the set of real numbers, is -quasi-Cauchy if , where , and is a lacunary sequence, that is, an increasing sequence of positive integers such that and . A new type compactness, namely, -ward compactness, is also, defined and some new results related to this kind of compactness are obtained.
Subject
Applied Mathematics,Analysis
Cited by
40 articles.
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