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Upper Bounds for Bernstein Basis Functions

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Prokhorov and Contemporary Probability Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 33))

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Abstract

From Markov’s bounds for binomial coefficients (for which a short proof is given) upper bounds are derived for Bernstein basis functions of approximation operators and their maximum. Some related inequalities used in approximation theory and those for concentration functions are discussed.

Mathematics Subject Classification (2010): 41A36, 41A44, 60E15, 60G50

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Acknowledgements

The authors thank very much Prof. Mamuka Jibladze who kindly found time to read the initial version of the manuscript, to discuss it with the second author and to prepare Figs. 1 and 2 using Mathematica.

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Authors and Affiliations

  1. School of Applied Sciences, Netaji Subhas Institute of Technology, Sector 3 Dwarka, New Delhi, 110078, India

    Vijay Gupta

  2. A. Razmadze Mathematical Institute, 1, M. Aleksidze St., Tbilisi, 0193, Georgia

    Tengiz Shervashidze

  3. I. Vekua Institute of Applied Mathematics, I. Javakhishvili Tbilisi State University, 2, University St., Tbilisi, 0186, Georgia

    Tengiz Shervashidze

Authors
  1. Vijay Gupta
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  2. Tengiz Shervashidze
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Corresponding author

Correspondence to Vijay Gupta .

Editor information

Editors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina Str. 8, Moscow, 119991, Russia

    Albert N. Shiryaev

  2. Courant Institute, New York University, Mercer Street 252, New York, 10012, New York, USA

    S. R. S. Varadhan

  3. Central Economics & Math. Institute, Russian Academy of Sciences, Nakhimovsky Pr. 47, Moscow, 117418, Russia

    Ernst L. Presman

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Gupta, V., Shervashidze, T. (2013). Upper Bounds for Bernstein Basis Functions. In: Shiryaev, A., Varadhan, S., Presman, E. (eds) Prokhorov and Contemporary Probability Theory. Springer Proceedings in Mathematics & Statistics, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33549-5_17

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