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Variation diminishing properties and convexity for the tensor product Bernstein operator

Part of the Lecture Notes in Mathematics book series (LNM,volume 1511)

Keywords

  • Bernstein Polynomial
  • Spline Surface
  • Bernstein Basis
  • Bernstein Basis Function
  • Variation Diminish

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References

  1. Geng-zhe Chang and Philip J. Davis, The convexity of Bernstein polynomials over triangles, J. Approximation Theory 40 (1984), 11–28.

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  2. Geng-zhe Chang and Yu-yu Feng, A new proof for convexity of Bernstein polynomials over triangles, to appear in Chinese Journal of Mathematics, Series B.

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  3. W. Dahmen and C.A. Micchelli, Convexity of multivariate Bernstein polynomials and box spline surfaces, Studia mathematicarum Hungarica 23(1988), 265–287.

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  4. G. Farin, Curves and Surfaces for Computer aided Geometic Design, Academic Press, N.Y., 1988.

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  5. T.N.T. Foodman, Variation diminishing properties of Bernstein polynomials on triangles, J. Approximation Theory 50 (1987), 111–126.

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Dedicated to the Memory of Professor U.N. Singh

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© 1992 Springer-Verlag

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Cavaretta, A.S., Sharma, A. (1992). Variation diminishing properties and convexity for the tensor product Bernstein operator. In: Yadav, B.S., Singh, D. (eds) Functional Analysis and Operator Theory. Lecture Notes in Mathematics, vol 1511. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093794

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  • DOI: https://doi.org/10.1007/BFb0093794

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55365-6

  • Online ISBN: 978-3-540-47041-0

  • eBook Packages: Springer Book Archive