On pointwise and uniform statistical convergence of order α for sequences of functions

Abstract

In this paper, we introduce the concepts of pointwise and uniform statistical convergence of order α for sequences of real-valued functions. Furthermore, we give the concept of an α-statistically Cauchy sequence for sequences of real-valued functions and prove that it is equivalent to pointwise statistical convergence of order α for sequences of real-valued functions. Also, some relations between S α (f)-statistical convergence and strong w β p (f)-summability are given. MSC: 40A05; 40C05; 46A45