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CALCOLO

, Volume 43, Issue 3, pp 151–170 | Cite as

The q-derivative and applications to q-Szász Mirakyan operators

  • Ali Aral
  • Vijay Gupta
Article

Abstract

By using the properties of the q-derivative, we show that q-Szász Mirakyan operators are convex, if the function involved is convex, generalizing well-known results for q = 1. We also show that q-derivatives of these operators converge to q-derivatives of approximated functions. Futhermore, we give a Voronovskaya-type theorem for monomials and provide a Stancu-type form for the remainder of the q-Szász Mirakyan operator. Lastly, we give an inequality for a convex function f, involving a connection between two nonconsecutive terms of a sequence of q-Szász Mirakyan operators.

Keywords

Hypergeometric Series Bernstein Polynomial Divided Difference Positive Linear Operator Bernstein Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Ali Aral
    • 1
  • Vijay Gupta
    • 2
  1. 1.Department of Mathematics, Faculty of Science and Arts, Kırıkkale University, KırıkkaleTurkey
  2. 2.School of Applied Sciences, Netaji Subhas Institute of Technology, Sector 3, DwarkaIndia

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