Standard

Bernstein-type inequalities for mean n-valent functions. / Баранов, Антон Дмитриевич; Каюмов, Ильгиз Рифатович; Zarouf, Rachid.

In: Journal of Approximation Theory, Vol. 311, 106200, 01.11.2025.

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

Harvard

Баранов, АД, Каюмов, ИР & Zarouf, R 2025, 'Bernstein-type inequalities for mean n-valent functions', Journal of Approximation Theory, vol. 311, 106200. https://doi.org/10.1016/j.jat.2025.106200

APA

Баранов, А. Д., Каюмов, И. Р., & Zarouf, R. (2025). Bernstein-type inequalities for mean n-valent functions. Journal of Approximation Theory, 311, [106200]. https://doi.org/10.1016/j.jat.2025.106200

Vancouver

Баранов АД, Каюмов ИР, Zarouf R. Bernstein-type inequalities for mean n-valent functions. Journal of Approximation Theory. 2025 Nov 1;311. 106200. https://doi.org/10.1016/j.jat.2025.106200

Author

Баранов, Антон Дмитриевич ; Каюмов, Ильгиз Рифатович ; Zarouf, Rachid. / Bernstein-type inequalities for mean n-valent functions. In: Journal of Approximation Theory. 2025 ; Vol. 311.

BibTeX

@article{5a353e33b2be404cb63e4f510b08bb34,
title = "Bernstein-type inequalities for mean n-valent functions",
abstract = "We derive new integral estimates of the derivatives of mean n-valent functions in the unit disc. Our results develop and complement estimates obtained by E.P. Dolzhenko and A.A. Pekarskii, as well as recent inequalities obtained by the authors. As an application, we improve some inverse theorems of rational approximation due to Dolzhenko.",
keywords = "Bernstein-type inequalities, Besov spaces, Hayman's inequality, Inverse theorems of rational approximation, n-valent functions",
author = "Баранов, {Антон Дмитриевич} and Каюмов, {Ильгиз Рифатович} and Rachid Zarouf",
year = "2025",
month = nov,
day = "1",
doi = "10.1016/j.jat.2025.106200",
language = "English",
volume = "311",
journal = "Journal of Approximation Theory",
issn = "0021-9045",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Bernstein-type inequalities for mean n-valent functions

AU - Баранов, Антон Дмитриевич

AU - Каюмов, Ильгиз Рифатович

AU - Zarouf, Rachid

PY - 2025/11/1

Y1 - 2025/11/1

N2 - We derive new integral estimates of the derivatives of mean n-valent functions in the unit disc. Our results develop and complement estimates obtained by E.P. Dolzhenko and A.A. Pekarskii, as well as recent inequalities obtained by the authors. As an application, we improve some inverse theorems of rational approximation due to Dolzhenko.

AB - We derive new integral estimates of the derivatives of mean n-valent functions in the unit disc. Our results develop and complement estimates obtained by E.P. Dolzhenko and A.A. Pekarskii, as well as recent inequalities obtained by the authors. As an application, we improve some inverse theorems of rational approximation due to Dolzhenko.

KW - Bernstein-type inequalities

KW - Besov spaces

KW - Hayman's inequality

KW - Inverse theorems of rational approximation

KW - n-valent functions

UR - https://www.mendeley.com/catalogue/255d69a5-6657-3bae-8d9f-485ccbb6b209/

U2 - 10.1016/j.jat.2025.106200

DO - 10.1016/j.jat.2025.106200

M3 - Article

VL - 311

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

M1 - 106200

ER -

ID: 136054934