On some spaces of almost lacunary convergent sequences derived by Riesz mean and weighted almost lacunary statistical convergence in a real n -normed space

摘要

In this paper, we introduce some new spaces of almost convergent sequences derived by Riesz mean and the lacunary sequence in a real n-normed space. By combining the definitions of lacunary sequence and Riesz mean, we obtain a new concept of statistical convergence which will be called weighted almost lacunary statistical convergence in a real n-normed space. We examine some connections between this notion with the concept of almost lacunary statistical convergence and weighted almost statistical convergence, where the base space is a real n-normed space. MSC:40C05, 40A35, 46A45, 40A05, 40F05.