Approximation of analytical functions by $$k$$ k -positive linear operators in the closed domain

Abstract

This work treats the problem of convergence for the sequences of linear $$k$$ -positive operators on a space of functions that are analytic in a closed domain. By convergence in this space, we mean a uniform convergence in a closed domain that contains the original domain strictly inside itself, while the linear $$k$$ -positive operators are naturally associated with Faber polynomials related to the considered domain. Until now, this problem has been solved in the space of functions analytic in an open bounded domain with the topology of compact convergence.