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Aequationes mathematicae

, Volume 90, Issue 4, pp 719–726 | Cite as

Best constant in stability of some positive linear operators

  • Dorian Popa
  • Ioan Raşa
Article

Abstract

We prove that the kernels of Bernstein, Stancu and Kantorovich operators are proximinal sets, therefore the infimum of Hyers–Ulam constants is also a Hyers–Ulam constant for the above mentioned operators. Moreover, we investigate what happens when the supremum norm is replaced by the L 1-norm.

Keywords

Hyers–Ulam stability best constant proximinal set 

Mathematics Subject Classification

39B82 41A35 41A44 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University of Cluj-NapocaCluj-NapocaRomania

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