Abel statistical quasi Cauchy sequences

Abstract

In this paper, we investigate the concept of Abel statistical quasi Cauchy sequences. A real function f is called Abel statistically ward continuous if it preserves Abel statistical quasi Cauchy sequences, where a sequence (?k) of point in R is called Abel statistically quasi Cauchy if limx?1-(1-x) ?k:|??k|?? xk = 0 for every ? > 0, where ??k = ?k+1-?k for every k ? N. Some other types of continuities are also studied and interesting results are obtained. It turns out that the set of Abel statistical ward continuous functions is a closed subset of the space of continuous functions.