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On the monotonicity of the sequence formed by the first order derivatives of the Bernstein polynomials

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References

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    Aramă, O.: Proprietăti privind monotonia sirului polinoamelor de interpolare ale luiS. N. Bernstein si aplicarea lor la studiul aproximârii functiilor. Acad. R. P. Rom. Fil. Cluj, Studii Cerc. Mat.8, 195–210 (1957). (This article has appeared in Russian translation [Mathematica2 (25) 25–40 (1960)].)

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    —, andD. Ripianu: Sur la monotonie de la suite des dérivées des polynomes de Bernstein. Mathematica4 (27), 9–19 (1962).

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    Popoviciu, T.: Les fonctions convexes. Actualités Sci. Ind., No. 992 (1944).

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    Schoenberg, I. J.: On variation diminishing approximation methods, p. 249–274. In: On numerical approximation, ed.R. E. Langer, Madison: The University of Wisconsin Press 1959.

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    Stancu, D. D.: The remainder of certain linear approximation formulas in two variables. Journ. SIAM Numer. Anal. Ser. B,1, 137–163 (1964).

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    Temple, W. B.: Stieltjes integral repersentation of convex functions. Duke Math. J.21, 527–531 (1954).

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Stancu, D.D. On the monotonicity of the sequence formed by the first order derivatives of the Bernstein polynomials. Math Z 98, 46–51 (1967). https://doi.org/10.1007/BF01116567

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Keywords

  • Order Derivative
  • Bernstein Polynomial