Lacunary statistical quasi-Cauchy sequences

Details Lacunary statistical quasi-Cauchy sequences Lacunary statistical quasi-Cauchy sequences

2011-02-08

arxiv.org/abs/1102.1531v1

Mathematics

Classical Analysis and ODEs

17 pages

Scientific paper

In this paper we call a real-valued function lacunarily statistically ward continuous if it preserves lacunary statistical quasi-Cauchy sequences where a sequence $(\alpha_{k})$ is defined to be lacunarily statistically quasi-Cauchy when the sequence $(\Delta \alpha_{k})$ is lacunarily statistically convergent to 0. We prove theorems related to lacunary statistical ward compactness, statistical ward compactness, lacunary statistical ward continuity, statistical ward continuity, ward continuity, and uniform continuity. It turns out that any lacunarily statistically ward continuous function on a lacunary statistically ward compact subset $A$ of \textbf{R} is uniformly continuous on $A$. We also prove some inclusion theorems between the set of lacunary statistical quasi-Cauchy sequences and the set of statistical quasi-Cauchy sequences.

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