From Uniform to Statistical Convergence of Binomial-Type Operators

  • Octavian AgratiniEmail author


Sequences of binomial operators introduced by using umbral calculus are investigated from the point of view of statistical convergence. This approach is based on a detailed presentation of delta operators and their associated basic polynomials. Bernstein–Sheffer linear positive operators are analyzed, and some particular cases are highlighted: Cheney–Sharma operators, Stancu operators, Lupaş operators.


Statistical convergence Binomial sequence Linear positive operator Umbral calculus Bernstein–Sheffer operator Pincherle derivative 

2010 Mathematics Subject Classification

05A40 41A36 47A58 


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania
  2. 2.Tiberiu Popoviciu Institute of Numerical AnalysisRomanian AcademyCluj-NapocaRomania

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