Statistical ward continuity

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