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 ? for sequences of real-valued functions. Furthermore, we give the concept of an ?-statistically Cauchy sequence for sequences of real-valued functions and prove that it is equivalent to pointwise statistical convergence of order ? for sequences of real-valued functions. Also, some relations between [InlineEquation not available: see fulltext.]-statistical convergence and strong [InlineEquation not available: see fulltext.]-summability are given. MSC: 40A05, 40C05, 46A45. © 2013 Çinar et al.; licensee Springer.