Abstract
In this paper we introduce the concepts of quasi-statistical limit point and quasi-statistical cluster point of a sequence. We give some inclusion results concerning these concepts. We also give the relationship between the Knopp core and quasi-statistical core of a sequence. Finally we state some theorems which deal with quasi-summability and quasi-statistical convergence of a sequence under some assumptions.
Highlights
The convergence of sequences has many generalizations with the aim of providing deeper insights into summability theory
In this paper we introduce the concepts of quasi-statistical limit point and quasi-statistical cluster point of a sequence
We give the relationship between the Knopp core and quasi-statistical core of a sequence
Summary
The convergence of sequences has many generalizations with the aim of providing deeper insights into summability theory. The number sequence x = (xk) is statistically convergent to L provided that for every " > 0 the set K" = fk 2 N : jxk Lj "g has natural density zero.
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