On statistical and strong convergence with respect to a modulus function and a power series method

Abstract

This paper introduces and focuses on two pairs of concepts in two main sections. The first section aims to examine the relation between the concepts of strong J_{p}-convergence with respect to a modulus function f and J_{p}-statistical convergence, where J_{p} is a power series method. The second section introduces the notions of f-J_{p}-statistical convergence and f-strong J_{p}-convergence and discusses some possible relations among them.