Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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IMPROVED BOUNDS OF POLYNOMIAL INEQUALITIES WITH RESTRICTED ZERO

  • Robinson Soraisam (Department of Mathematics, National Institute of Technology Manipur) ;
  • Nirmal Kumar Singha (Department of Mathematics, National Institute of Technology Manipur) ;
  • Barchand Chanam (Department of Mathematics, National Institute of Technology Manipur)
  • Received : 2022.08.10
  • Accepted : 2022.10.18
  • Published : 2023.06.15
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Abstract

Let p(z) be a polynomial of degree n having no zero in |z| < k, k ≥ 1. Then Malik [12] obtained the following inequality: $${_{max \atop {\mid}z{\mid}=1}{\mid}p{\prime}(z){\mid}{\leq}{\frac{n}{1+k}}{_{max \atop {\mid}z{\mid}=1}{\mid}p(z){\mid}.$$ In this paper, we shall first improve as well as generalize the above inequality. Further, we also improve the bounds of two known inequalities obtained by Govil et al. [8].

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Acknowledgement

We are thankful to NIT, Manipur for providing us financial support. We are also grateful to the referee for his/her useful suggestions.

References

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