Approximation of analytical functions by \(k\) -positive linear operators in the closed domain

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• 作者：Akif D. Gadjiev (1)
  Rashid A. Aliev (2)
  
• 关键词：Linear $$k$$ k ; positive operators ; Faber polynomials ; Conformal mapping ; Analytic functions ; Statistical approximation ; Korovkin type theorem ; 47A58 ; 47B65
• 刊名：Positivity
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：18
• 期：3
• 页码：439-447
• 全文大小：184 KB
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• 作者单位：Akif D. Gadjiev (1)
  Rashid A. Aliev (2)
  
  1. Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, B. Vaxabzadeh str. 9, 1141, 聽Baku, Azerbaijan
  2. Faculty of Mechanics-Mathematics, Baku State University, Z. Khalilov str. 23, 1148聽, Baku, Azerbaijan
  
• ISSN：1572-9281

文摘

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.