Relations Between the Bernstein Polynomials and q-monotone Functions-Reference-Cited by-同舟云学术

Relations Between the Bernstein Polynomials and q-monotone Functions

Published:2022-10-29 Issue:6 Volume:77 Page:
ISSN:1422-6383
Container-title:Results in Mathematics
language:en
Short-container-title:Results Math

Author:

Abel Ulrich,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 ] , imply that the function is q-monotone. In view of previous results of the authors (see the list of references), the current results provide, among others, a characterization of q-monotone functions in C[0, 1].

Funder

Technische Hochschule Mittelhessen

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Mathematics (miscellaneous)

Link

https://link.springer.com/content/pdf/10.1007/s00025-022-01764-8.pdf

Reference9 articles.

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

4. Davis, P.J.: Interpolation & Approximation. Dover publications Inc., New York (1975)

5. Gavrea, B., Gavrea, I.: An inequality involving Bernstein polynomials and boxconvex functions. Med. J. Math. 19(18), 1–15 (2022)

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