I-convergence theorems for a class of k-positive linear operators

Abstract

Abstract:In this paper, we obtain some approximation theorems for -positive linear operators defined on the space of analytical functions on the unit disc, via −convergence. Some concluding remarks which includes A−statistical convergence are also given. MSC:41A10, 41A25, 41A36, 40A25

On ideal convergence of sequences of linear operators in the space of analytic functions

“…In the paper [11] , the authors firstly proved the Korovkin type theorems on statistical approximation and also gave the definition of order of statistical approximation by positive linear operators. Recently, some different versions of statistical approximation by k−positive linear operators were obtained in [2,16] . Inspired by the recent works on these topics, we investigate the problem of approximation of analytic functions and their derivatives by the sequences of linear operators and their derivatives acting on the space of analytic functions in a simply connected bounded domain without properties of k−positivity, via ideal convergence.…”

Approximation of analytic functions by sequences of linear operators

“…Using this definition of k−positivity in [4], some results on approximation of analytic functions in the unit disk by means of k−positive linear operators were obtained. Then, various approximation problems of analytic functions by k−positive linear operators have been studied intensively by several authors (see [1], [2], [5]- [10]). We may remark here that recently, general theorems were proved for linear operators acting on the space of analytic functions in a simply connected bounded domain in [6].…”