A variation on Abel quasi Cauchy sequences.

In this paper, we introduce and investigate the concept of Abel ward continuity. A real function ƒ is Abel ward continuous if it preserves Abel quasi Cauchy sequences, where a sequence (pk) of point in R is called Abel quasi-Cauchy if the series Σk=0∞△pk·xk is convergent for 0 ≤ x < 1 and limx→1-(1-x)Σk=0∞△pk·xk=0, where → pk = pk+1 - pk for every non negative integer k. Some other types of continuities are also studied and interesting results are obtained. It turns out that uniform limit of a sequence of Abel ward continuous functions is Abel ward continuous and the set of Abel ward continuous functions is a closed subset of the set of continuous functions. [ABSTRACT FROM AUTHOR]