Asymptotic Evaluations for Some Sequences of Positive Linear Operators

Abstract

We prove asymptotic evaluations for univariate and multivariate positive linear operators. Our proofs are different from what has been used so far. As applications of our results, we find the full asymptotic evaluation for the iterates of the univariate Cesaro and Volterra operators. Moreover, we find asymptotic evaluations for the iterates of multivariate Cesaro and Volterra type operators on the k-dimensional unit cube, k-dimensional unit triangle, etc.