Density by Moduli and statistical convergence

Abstract

By using modulus functions we introduce a new concept of density for sets of natural numbers. Consequently, we obtain a generalization of the notion of statistical convergence which is studied and characterized. As an application, we prove that the ordinary convergence is equivalent to the module statistical convergence for every unbounded modulus function.

Keywords: Density, modulus function, statistical convergence.

Quaestiones Mathematicae 37(2014), 525-530