Remarks on q-Monotone Functions and the Bernstein polynomials

Ulrich Abel; Dany Leviatan; Ioan Raşa

doi:10.1007/s00025-022-01810-5

Remarks on q-Monotone Functions and the Bernstein polynomials

Ulrich Abel^*
, Dany Leviatan
, Ioan Raşa

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We show that certain inequalities involving differences of the Bernstein basis polynomials and values of a function 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.

Original language	English
Article number	41
Journal	Results in Mathematics
Volume	78
Issue number	2
DOIs	https://doi.org/10.1007/s00025-022-01810-5
State	Published - Apr 2023

Keywords

Polynomial inequalities
functional inequalities
q-monotonicity

Access to Document

10.1007/s00025-022-01810-5

Cite this

@article{787d42269313480e8abd727dd40d48d6,

title = "Remarks on q-Monotone Functions and the Bernstein polynomials",

abstract = "We show that certain inequalities involving differences of the Bernstein basis polynomials and values of a function 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.",

keywords = "Polynomial inequalities, functional inequalities, q-monotonicity",

author = "Ulrich Abel and Dany Leviatan and Ioan Ra{\c s}a",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2023",

month = apr,

doi = "10.1007/s00025-022-01810-5",

language = "אנגלית",

volume = "78",

journal = "Results in Mathematics",

issn = "1422-6383",

publisher = "Birkhauser",

number = "2",

}

TY - JOUR

T1 - Remarks on q-Monotone Functions and the Bernstein polynomials

AU - Abel, Ulrich

AU - Leviatan, Dany

AU - Raşa, Ioan

PY - 2023/4

Y1 - 2023/4

N2 - We show that certain inequalities involving differences of the Bernstein basis polynomials and values of a function 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.

AB - We show that certain inequalities involving differences of the Bernstein basis polynomials and values of a function 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.

KW - Polynomial inequalities

KW - functional inequalities

KW - q-monotonicity

UR - https://www.scopus.com/pages/publications/85144320214

U2 - 10.1007/s00025-022-01810-5

DO - 10.1007/s00025-022-01810-5

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85144320214

SN - 1422-6383

VL - 78

JO - Results in Mathematics

JF - Results in Mathematics

IS - 2

M1 - 41

ER -

Remarks on q-Monotone Functions and the Bernstein polynomials

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this