Nonlinear Functional Analysis and Applications

  • 제27권1호
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  • Pages.141-148
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  • 2022
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  • 1229-1595(pISSN)
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  • 2466-0973(eISSN)
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
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SOME INEQUALITIES ON POLAR DERIVATIVE OF A POLYNOMIAL

  • 투고 : 2021.05.20
  • 심사 : 2021.12.08
  • 발행 : 2022.03.15
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⟨ 이전 논문 다음 논문 ⟩

초록

Let p(z) be a polynomial of degree n having no zero in |z| < k, k ≤ 1, then Govil proved $$\max_{{\mid}z{\mid}=1}{\mid}p^{\prime}(z){\mid}{\leq}{\frac{n}{1+k^n}}\max_{{\mid}z{\mid}=1}{\mid}p(z){\mid}$$, provided |p'(z)| and |q'(z)| attain their maximal at the same point on the circle |z| = 1, where $$q(z)=z^n{\overline{p(\frac{1}{\overline{z}})}}$$. In this paper, we extend the above inequality to polar derivative of a polynomial. Further, we also prove an improved version of above inequality into polar derivative.

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참고문헌

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