Approximation of analytic functions by sequences of linear operators

Abstract

In the present paper, we investigate approximation of analytic functions and their derivatives in a bounded simply connected domain by the sequences of linear operators without the properties of k−positivity.

Approximation of analytic functions of severalvariables by linear k-positive operators

“…He introduced k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc. He proposed a method of proving such theorems, applied further on in many other articles (e.g., [1,3,[6][7][8][9][10][11][12][13]15,16]). Some of the results from [1,[5][6][7] were included in a monograph [2,14].…”