Abel statistical convergence in metric spaces

Abstract

In this study, we investigate the concepts of Abel statistical convergence and Abel statistical quasi Cauchy sequences. A function f from a subset E of a metric space X into X is called Abel statistically ward continuous it preserves Abel statistical quasi Cauchy sequences, where a sequence (xk) of point in E is called Abel statistically quasi Cauchy if limx→1− (1 − x) ∑ k:d(xk+1,xk)≥ε x k = 0 for every ε > 0. Some other types of continuities are also studied and interesting results are obtained.