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 (α k) of point in R is called Abel statistically quasi Cauchy if lim x→1 − (1 − x) k:|∆α k | ε x k = 0 for every ε > 0, where ∆α k = α k+1 − α 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.