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Variation diminishing properties and convexity for the tensor product Bernstein operator

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Functional Analysis and Operator Theory

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

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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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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Alberta

    A. S. Cavaretta Jr. & A. Sharma

  2. Department of Mathematics, Kent State University, 44214, Kent, Ohio, USA

    A. S. Cavaretta Jr. & A. Sharma

Authors
  1. A. S. Cavaretta Jr.
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  2. A. Sharma
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Editor information

B. S. Yadav D. Singh

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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

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