Remarks on q-Monotone Functions and the Bernstein polynomials

Author:

Abel UlrichORCID,Leviatan Dany,Raşa Ioan

Abstract

AbstractWe show that certain inequalities involving differences of the Bernstein basis polynomials and values of a function $$f\in C[0,1]$$ f C [ 0 , 1 ] , which is twice differentiable in [0, 1], imply that the function is q-monotone. This provides a partial answer to an open problem of the authors in a recent paper.

Funder

Technische Hochschule Mittelhessen

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Mathematics (miscellaneous)

Reference6 articles.

1. Abel, U.: An inequality involving Bernstein polynomials and convex functions. J. Approx. Theory 222, 1–7 (2017)

2. Abel, U., Leviatan, D.: An extension of Raşa’s conjecture to $$q$$-monotone functions. Results Math. 75:180, 1–13 (2020)

3. Abel, U., Leviatan, D., Raşa, I.: Relations between the Bernstein polynomials and $$q$$-monotone functions. Results Math. 77:239, 1–12 (2022)

4. Abel, U., Raşa, I.: A sharpening of a problem on Bernstein polynomials and convex functions. Math. Inequ. Appl. 21, 773–777 (2018)

5. Lorentz, G.G.: Bernstein polynomials, Mathematical Expositions, No. 8., University of Toronto Press, Toronto, (1953)

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