On Abel statistical convergence

Abstract

In this paper, we introduce and investigate a concept of Abel statistical continuity. A real valued function $f$ is Abel statistically continuous on a subset $E$ of $\mathbb{R}$, the set of real numbers, if it preserves Abel statistical convergent sequences, i.e. $(f(p_k))$ is Abel statistically convergent whenever $(p_k)$ is an Abel statistical convergent sequence of points in $E$, where a sequence $(p_k)$ of point in $\mathbb{R}$ is called Abel statistically convergent to a real number $L$ if Abel density of the set $\{k\in \mathbb{N}:|p_k-L|\ge \epsilon \}$ is $0$ for every $\epsilon >0$. Some other types of continuities are also studied and interesting results are obtained.

11 pages. arXiv admin note: text overlap with arXiv:1101.1440

References in corpus (1)

• Functions preserving slowly oscillating double sequences