$f-$statistical convergence, completeness and $f-$cluster points

Abstract

We study $f-$statistical convergence, which is a generalization of the classical statistical convergence. In terms of it, we give a characterization of completeness in a normed space. We also introduce `$f-$statistical cluster points', which is a richer concept than the classic one. Namely, each (usual) limit point of a sequence is an $f-$statistical cluster point for some $f$.