On Abel statistical convergence
Iffet Taylan, Huseyin Cakalli

TL;DR
This paper introduces the concept of Abel statistical continuity, studying functions that preserve Abel statistically convergent sequences and exploring related types of continuity with new results.
Contribution
It defines Abel statistical continuity and investigates its properties, establishing its relationship with other forms of continuity in real analysis.
Findings
Abel statistical continuous functions preserve Abel statistical convergence.
The paper establishes properties and relationships with other continuity types.
New results on the behavior of Abel statistical continuous functions are presented.
Abstract
In this paper, we introduce and investigate a concept of Abel statistical continuity. A real valued function is Abel statistically continuous on a subset of , the set of real numbers, if it preserves Abel statistical convergent sequences, i.e. is Abel statistically convergent whenever is an Abel statistical convergent sequence of points in , where a sequence of point in is called Abel statistically convergent to a real number if Abel density of the set is for every . Some other types of continuities are also studied and interesting results are obtained.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Fuzzy and Soft Set Theory · Advanced Banach Space Theory
