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Chlodowsky type generalization of (pq)-Szász operators involving Brenke type polynomials

  • Uğur Kadak
  • Vishnu Narayan Mishra
  • Shikha Pandey
Original Paper

Abstract

In this paper, we introduce a Chlodowsky variant of the Szász operators by means of the (pq)-integers as well as of the (pq)-Gaussian binomial coefficients. For\(0< q <p \le 1,\) we denote the sequence of (pq)-Szász operators by \(L_{n,p, q}\) and obtain some direct theorems and results based on statistical convergence. Furthermore, we show comparisons and some illustrative graphics for the convergence of operators to a function.

Keywords

\((p, q)\)-Szász type operators involving Brenke type polynomials Korovkin and Voronovskaja type approximation theorems Rate of convergence Weighted approximation 

Mathematics Subject Classification

Primary 41A10 41A25 41A36 Secondary 40A25 11B83 

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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  • Uğur Kadak
    • 1
  • Vishnu Narayan Mishra
    • 2
    • 3
    • 4
  • Shikha Pandey
    • 3
  1. 1.Department of MathematicsGazi UniversityAnkaraTurkey
  2. 2.FaizabadIndia
  3. 3.Applied Mathematics and Humanities DepartmentSardar Vallabhbhai National Institute of TechnologySuratIndia
  4. 4.Department of MathematicsIndira Gandhi National Tribal UniversityAmarkantakIndia

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