Rates of A-statistical convergence of positive linear operators

In the classical summability setting rates of summation have been introduced in several ways (see, e.g., [10], [21], [22]). The concept of statistical rates of convergence, for nonvanishing two null sequences, is studied in [13]. Unfortunately no single de...nition seems to have become the “standard” for the comparison of rates of summability transforms. The situation becomes even more uncharted when one considers rates of A¡statistical convergence. For this reason various ways of de...ning rates of convergence in the A¡statistical sense are introduced in [6]. In the present paper, using the concepts of [6], we study rates of A¡statistical convergence of sequences of positive linear operators mapping the weighted space C1⁄21 into the weighted space B1⁄22 where 1⁄21 and 1⁄22 are weight functions satisfying the condition lim jxj!1 1⁄21(x) 1⁄22(x) = 0;