Variations on Statistical Quasi Cauchy Sequences

In this paper, we introduce a concept of statistically p-quasi-Cauchyness of a real sequence in the sense that a sequence (alpha(k)) is statistically p-quasi-Cauchy if lim(n) (->infinity)1/n vertical bar {k <= n : vertical bar alpha(k+p) - alpha(k)vertical bar >= epsilon}vertical bar = 0 for each epsilon > 0. A function f is called statistically p-ward continuous on a subset A of the set of real umbers R if it preserves statistically p-quasi-Cauchy sequences, i.e. the sequence f (x) = (f (alpha(n))) is statistically p-quasi-Cauchy whenever alpha = (alpha(n)) is a statistically p-quasi-Cauchy sequence of points in A. It turns out that a real valued function f is uniformly continuous on a bounded subset, A of R if there exists a positive integer p such that, f preserves statistically p-quasi-Cauchy sequences of points in A.