Kyungpook Mathematical Journal

  • 제55권4호
  • /
  • Pages.807-816
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  • 2015
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On Zeros of Polynomials with Restricted Coefficients

  • RASOOL, TAWHEEDA (Department of Mathematics, National Institute of Technology) ;
  • AHMAD, IRSHAD (Department of Mathematics, National Institute of Technology) ;
  • LIMAN, AB (Department of Mathematics, National Institute of Technology)
  • 투고 : 2013.05.21
  • 심사 : 2013.08.07
  • 발행 : 2015.12.23
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초록

Let $P(z)={\limits\sum_{j=0}^{n}}a_jz^j$ be a polynomial of degree n and Re $a_j={\alpha}_j$, Im $a_j=B_j$. In this paper, we have obtained a zero-free region for polynomials in terms of ${\alpha}_j$ and ${\beta}_j$ and also obtain the bound for number of zeros that can lie in a prescribed region.

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참고문헌

  1. G. Enestrom, Remarquee sur un Theorem relative aux racinnes de I'equation $a_{n}z^{n}+a_{n-1}z^{n-1}+...a_{1}+a_{0}$ ou to us les coefficients sonts reels et possitifs, Tohoku Math. J., 18(1920), 34-36.
  2. M. Marden, The Geometry of polynomials, Amer. Math. Monthly, 83(10)(1997), 788-797. https://doi.org/10.2307/2318685
  3. Q. G. Mohammad, On the zeros of the polynomials, Amer. Math. Monthly, 72(6)(1965), 631-633. https://doi.org/10.2307/2313853
  4. S. Kakeya, On the limits of the roots of an algebraic equation with positive coefficients, Tohoku Math. J., 2(1912-13), 140-142.
  5. E. C. Titchmarsh, The theory of functions, 2nd ed. Oxford Univ. Press, London, (1939).