Interpolation Function of Generalized q −Bernstein-Type Basis Polynomials and Applications

  • Yilmaz Simsek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6920)


The main aim of this paper is to construct a new generating function for the generalized q-Bernstein-type basis polynomials and to derive fundamental properties of these polynomials. We establish relations between the generalized q-Bernstein-type basis polynomials, the Bernoulli polynomials of higher-order and the generalized Stirling numbers of the second kind. By applying Mellin transform to this generating function, we also construct an interpolating function, which interpolates the generalized q-Bernstein-type basis polynomials at negative integers. Furthermore, we give applications on the generalized q-Bernstein-type basis polynomials and the Bézier curves.


Bernstein basis polynomials Generating function q- Bernstein basis polynomials Bernoulli polynomials of higher-order Stirling numbers of the second kind interpolating function Mellin transform Gamma function beta function Bézier curves 


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yilmaz Simsek
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceUniversity of AkdenizAntalyaTurkey

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