Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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SOME INEQUALITIES ON POLAR DERIVATIVE OF A POLYNOMIAL

  • N., Reingachan (Department of Mathematics, National Institute of Technology Manipur) ;
  • Robinson, Soraisam (Department of Mathematics, National Institute of Technology Manipur) ;
  • Barchand, Chanam (Department of Mathematics, National Institute of Technology Manipur)
  • Received : 2022.01.07
  • Accepted : 2022.03.18
  • Published : 2022.12.06
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Abstract

Let P(z) be a polynomial of degree n. A well-known inequality due to S. Bernstein states that if P ∈ Pn, then $$\max_{{\mid}z{\mid}=1}\,{\mid}P^{\prime}(z){\mid}\,{\leq}n\,\max_{{\mid}z{\mid}=1}\,{\mid}P(z){\mid}$$. In this paper, we establish some extensions and refinements of the above inequality to polar derivative and some other well-known inequalities concerning the polynomials and their ordinary derivatives.

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Acknowledgement

We are grateful to the referees for their valuable suggestions.

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