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Abstract <p>This work is a part of recent wave of studies on inequalities which relate the uniform-norm of a complex polynomial to its derivative on the unit disk in the plane. When there is a limit on the zeros of a polynomial, we develop some generalized inequalities that relate the uniform-norm of the polynomial to its derivative. In this paper, we use the zero-preserving property of the derivative on the space of complex polynomials and thereby estimate some Bernstein-type inequalities for polynomials.</p>

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Application of Gauss–Lucas Theorem to the Inequalities for Polynomials

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • M. Y. Mir,
  • W. M. Shah

摘要

Abstract

This work is a part of recent wave of studies on inequalities which relate the uniform-norm of a complex polynomial to its derivative on the unit disk in the plane. When there is a limit on the zeros of a polynomial, we develop some generalized inequalities that relate the uniform-norm of the polynomial to its derivative. In this paper, we use the zero-preserving property of the derivative on the space of complex polynomials and thereby estimate some Bernstein-type inequalities for polynomials.