On statistical convergence with respect to power series methods

Abstract

In this paper, we establish a relationship between the concepts of P-strong, P-statistical convergences and P-uniform integrability where P stands for a power series method. We also prove that if a power series method has a summability function, then the space of all P-statistically convergent sequences cannot be endowed with a local convex FK-topology. We finally study P-statistical convergence in a Hausdorff topological space and investigate the relationships among these concepts and weak convergence of Baire measures.