Scholarlink

<p>Recently, Rather et al. (Rend Circ Mat Palermo II Ser 70:1201, 2020) considered the generalized polar derivative and studied the relative position of zeros of the generalized polar derivative with respect to the zeros of the polynomial. In this paper, we obtain some lower bound estimates for the generalized polar derivative of certain polynomials with restricted zeros. Furthermore, we prove some <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40627_2025_153_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>—inequalities for the generalized derivative of a polynomial having zeros in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40627_2025_153_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="100" /> </InlineMediaObject> <EquationSource Format="TEX">\(|z| \le \zeta , \zeta \le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mi>z</mi> <mo stretchy="false">|</mo> <mo>≤</mo> <mi>ζ</mi> <mo>,</mo> <mi>ζ</mi> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Turán-type inequalities for generalized polar derivative of complex polynomials

  • 期刊论文

  • 发表日期：

    2025年4月10日

查看全文
  • Urba Akhter,
  • Abdul Liman

摘要

Recently, Rather et al. (Rend Circ Mat Palermo II Ser 70:1201, 2020) considered the generalized polar derivative and studied the relative position of zeros of the generalized polar derivative with respect to the zeros of the polynomial. In this paper, we obtain some lower bound estimates for the generalized polar derivative of certain polynomials with restricted zeros. Furthermore, we prove some \(L_{p}\) L p —inequalities for the generalized derivative of a polynomial having zeros in \(|z| \le \zeta , \zeta \le 1\) | z | ≤ ζ , ζ ≤ 1 .