On statistical convergence in modular vector spaces

Abstract

This paper extends the statistical convergence of real or complex numbers to the elements of a modular vector space equipped with a convex modular. In this context, we investigate the relation between the statistical convergence, statistical Cauchy condition, strong Cesàro summability, and $\rho$-convergence. This leads us to an initial analysis of the Tauberian conditions for the statistical convergence in the modular sense. We touch on an application to the fixed point theory via the ergodic theory.