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February 9, 2026Filomat0 citationsOpen Access

On the behavior of the modulus of m-th derivatives of algebraic polynomials in the whole complex plane without recurrence formula in the weighted Lebesgue space

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FAF.G. AbdullayevMersin ÜniversitesiMIM. ImashkyzyKyrgyz-Türkish Manas Üniversity

Key Points

  • The research aims to investigate how the m-th derivatives of algebraic polynomials behave in different regions of the complex plane without using recurrence formulas.
  • Analyzed growth of m-th derivatives of algebraic polynomials
  • Studied behavior in both bounded and unbounded regions
  • Provided estimates throughout the complex plane
  • Identified key growth patterns of derivatives in weighted Lebesgue spaces
  • Provided comprehensive estimates for the entire complex plane

Abstract

In this paper we study the growth of m-th derivatives of an arbitrary algebraic polynomial in weighted Lebesgue spaces in bounded and unbounded regions of the complex plane, ignoring the recurrence formula. We also provide estimates in the whole complex plane.

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Cite This Study

Abdullayev et al. (2025) studied this question.

synapsesocial.com/papers/698979f5f0ec2af6756e80adhttps://doi.org/10.2298/fil2510365a
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