Statistical ward continuity

Recently, it has been proved that a real-valued function defined on an interval AA of R, the set of real numbers, is uniformly continuous on AA if and only if it is defined on AA and preserves quasi-Cauchy sequences of points in AA. In this paper we call a real-valued function statistically ward continuous if it preserves statistical quasi-Cauchy sequences where a sequence (αk)(αk) is defined to be statistically quasi-Cauchy if the sequence (Δαk) is statistically convergent to 0. It turns out that any statistically ward continuous function on a statistically ward compact subset AA of R is uniformly continuous on AA. We prove theorems related to statistical ward compactness, statistical compactness, continuity, statistical continuity, ward continuity, and uniform continuity.