Abel statistical quasi Cauchy sequences

4th International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM) -- MAY 11-15, 2017 -- Aydin, TURKEY
WOS: 000464504500018
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 (alpha(k)) of point in R is called Abel statistically quasi Cauchy if lim(x -> 1)-(1 - x) Sigma(k:vertical bar Delta alpha k vertical bar >=epsilon) x(k) = 0 for every epsilon > 0, where Delta alpha(k) = alpha(k+1) - alpha(k) for every k is an element of 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.