Iterates of positive linear operators and linear systems of equations

When studying the iterates of certain positive linear operators, systems of linear equations are naturally involved. The last step in investigating the limit of such iterates is represented by a special kind of system of equations. Problems of this type involving several classical operators are studied in the literature. In this paper, we investigate the iterates of new positive linear operators and the corresponding systems of equations. To solve the system we use an iterative algorithm. The approximate solution is used in order to approximate the limit of the iterates of operators.