Results in Mathematics

, 74:13 | Cite as

An Answer to an Open Problem on the Multivariate Bernstein Polynomials on a Simplex

  • Ioan Gavrea
  • Mircea IvanEmail author


We answer and generalize an open problem on the two-dimensional Bernstein polynomials on the unit triangle.


Multivariate Bernstein polynomials simplex convexity 

Mathematics Subject Classification

32E20 41A36 41A17 42A16 



  1. 1.
    Abel, U., Gawronski, W., Neuschel, T.: Complete monotonicity and zeros of sums of squared Baskakov functions. Appl. Math. Comput. 258, 130–137 (2015). MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Altomare, F., Campiti, M.: Korovkin-type approximation theory and its applications, De Gruyter Studies in Mathematics, vol. 17. Walter de Gruyter & Co., Berlin (1994). (Appendix A by Michael Pannenberg and Appendix B by Ferdinand Beckhoff)
  3. 3.
    Gavrea, I., Ivan, M.: On a conjecture concerning the sum of the squared Bernstein polynomials. Appl. Math. Comput. 241, 70–74 (2014)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Gavrea, I., Ivan, M.: On a new sequence of positive linear operators related to squared Bernstein polynomials. Positivity 21(3), 911–917 (2017). MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Gonska, H., Raşa, I., Rusu, M.D.: Chebyshev-Grüss-type inequalities via discrete oscillations. Bul. Acad. Ştiinţe Repub. Mold. Mat. 1, 63–89 (2014)zbMATHGoogle Scholar
  6. 6.
    Nikolov, G.: Inequalities for ultraspherical polynomials. Proof of a conjecture of I. Raşa. J. Math. Anal. Appl. 418(2), 852–860 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Raşa, I.: Convexity properties of some entropies. Results Math. 73(3), 105 (2018). MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Technical University of Cluj NapocaCluj-NapocaRomania

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