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

Abstract

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