On statistical convergence of order ? of difference sequence of functions

In this paper we introduce the concepts of uniform and pointwise ?m - statistical convergence of order ? of sequence of functions. We also give notions of uniform and pointwise ?m -statistically Cauchy sequence of order ? of sequence of functions and show that pointwise ?m -statistically Cauchy sequence (uniform ?m -statistical convergence) is equivalent to pointwise ?m -statistical convergence (uniform ?m -statistically Cauchy sequence) of order ?. Moreover, some relations between pointwise ?m-statistical convergence of order ? and strongly pointwise ?mq -Cesàro summable of order ? of sequence of functions are given. © 2007 Maejo University, San Sai, Chiang Mai, 50290 Thailand