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Positivity

, Volume 18, Issue 3, pp 439–447 | Cite as

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

  • Akif D. Gadjiev
  • Rashid A. AlievEmail author
Article

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.

Keywords

Linear \(k\)-positive operators Faber polynomials Conformal mapping Analytic functions Statistical approximation Korovkin type theorem 

Mathematics Subject Classification (2000)

47A58 47B65 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Institute of Mathematics and MechanicsAzerbaijan National Academy of Sciences BakuAzerbaijan
  2. 2.Faculty of Mechanics-MathematicsBaku State UniversityBakuAzerbaijan

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