On statistical convergence of order. of difference sequence of functions

Abstract

In this paper we introduce the concepts of uniform and pointwise Delta(m) - statistical convergence of order alpha of sequence of functions. We also give notions of uniform and pointwise Delta(m) - statistically Cauchy sequence of order alpha of sequence of functions and show that pointwise Delta(m) - statistically Cauchy sequence (uniform Delta(m) -statistical convergence) is equivalent to pointwise Delta(m) - statistical convergence (uniform Delta(m) - statistically Cauchy sequence) of order alpha. Moreover, some relations between pointwise Delta(m) - statistical convergence of order alpha and strongly pointwise Delta(m)(q) - Cesaro summable of order alpha of sequence of functions are given.