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

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Curves and Surfaces (Curves and Surfaces 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6920))

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Akdeniz, TR-07058, Antalya, Turkey

    Yilmaz Simsek

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  1. Yilmaz Simsek
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Editor information

Editors and Affiliations

  1. INRIA Sophia-Antipolis, 2004 Route des Lucioles, BP 93, 06902, Sophia Antipolis, France

    Jean-Daniel Boissonnat

  2. Laboratoire LJK, University Joseph Fourier, BP 53, 38420, Grenoble Cedex 9, France

    Patrick Chenin

  3. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, Place Jussieu, 75005, Paris, France

    Albert Cohen

  4. Laboratoire de Mathématiques, INSA Rouen, Avenue de l’Université, 76800, St. Etienne du Rouvray, France

    Christian Gout

  5. University of Oslo, DMA, Blindern, P.O.Box 1053, 0316, Oslo, Norway

    Tom Lyche

  6. Laboratoire LJK, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

  7. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry Schumaker

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Simsek, Y. (2012). Interpolation Function of Generalized q −Bernstein-Type Basis Polynomials and Applications. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_43

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  • DOI: https://doi.org/10.1007/978-3-642-27413-8_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27412-1

  • Online ISBN: 978-3-642-27413-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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