, Volume 18, Issue 3, pp 585–594 | Cite as

Approximation in Banach space by linear positive operators

  • Arash GhorbanalizadehEmail author
  • Yoshihiro Sawano


In this paper, we obtain a sufficient condition for the convergence of positive linear operators in Banach function spaces on \({\mathbb {R}}^n\) and derive a Korovkin type theorem for these spaces. Also, we generalized this result via statistical sense.


Korovkin’s theorem Banach function spaces Positive linear operators 

Mathematics Subject Classification (2010)

Primary 42E35 



The research of Y. Sawano was supported by Grant-in-Aid for Young Scientists (B) (No.21740104) Japan Society for the Promotion of Science.


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsInstitute for Advanced Studies in Basic Sciences (IASBS)ZanjanIran
  2. 2.Department of Mathematics and Information ScienceTokyo Metropolitan UniversityTokyoJapan

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