Work

On the behavior of $$m-th$$ derivatives of polynomials in bounded and unbounded regions without zero angles in weighted Lebesgue spaces

Year: 2025

Type: article

Abstract: In this paper, we study the growth of the $$m-th$$ m - t h ( $$m\ge 1$$ m ≥ 1 ) derivatives of an arbitrary algebraic polynomial in weighted Lebesgue spaces over the whole complex plane. We first study the growth of the $$m-th$$ m - t h derivatives of an arbitrary algebraic polynomial over unbounded regions of the complex plane, and then we obtain estimates for the growth of the $$m-th$$ m - t h derivatives of this polynomial over the closure of the given region. Combining both estimates, we find estimates for the growth of the $$m-th$$ m - t h derivatives of an arbitrary algebraic polynomial over the whole complex plane.

Source: Analysis and Mathematical Physics

DOI: 10.1007/s13324-025-01055-9

Authors: F. G. Abdullayev, M. Imashkyzy

Institutions: Institute of Mathematics and Mechanics, Mersin Üniversitesi, Kyrgyz-Türkish Manas Üniversity

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Mersin Üniversitesi