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<p>Suppose <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(r(z)=p(z)/w(z),\)</EquationSource> </InlineEquation> where <i>p</i>(<i>z</i>) is a polynomial of degree at most <i>n</i> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(w(z)=\prod _{j=1}^{n}(z-a_{j}),\)</EquationSource> </InlineEquation> <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(|a_{j}|&gt;1\)</EquationSource> </InlineEquation> for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(1 \le j \le n.\)</EquationSource> </InlineEquation> In this paper, we consider the class of rational functions having a <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(t-\)</EquationSource> </InlineEquation>fold zero at some point inside the unit disk and prove certain results.</p>

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Generalized Bernstein-type inequalities for rational functions with restriction on zeros and poles

  • 期刊论文

  • 发表日期：

    2025年11月3日

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  • Raihana Rashid,
  • W. M. Shah

摘要

Suppose \(r(z)=p(z)/w(z),\) where p(z) is a polynomial of degree at most n and \(w(z)=\prod _{j=1}^{n}(z-a_{j}),\) \(|a_{j}|>1\) for \(1 \le j \le n.\) In this paper, we consider the class of rational functions having a \(t-\) fold zero at some point inside the unit disk and prove certain results.