한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제31권1호
  • /
  • Pages.49-56
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  • 2024
  • /
  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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SOME BOUNDS FOR ZEROS OF A POLYNOMIAL WITH RESTRICTED COEFFICIENTS

  • Mahnaz Shafi Chishti (School of Basic and Applied Sciences, Shobhit Institute of Engineering and Technology (Deemed to be University)) ;
  • Vipin Kumar Tyagi (School of Basic and Applied Sciences, Shobhit Institute of Engineering and Technology (Deemed to be University)) ;
  • Mohammad Ibrahim Mir (Department of Mathematics, University of Kashmir, South Campus)
  • 투고 : 2023.07.03
  • 심사 : 2023.12.11
  • 발행 : 2024.02.28
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초록

For a Polynomial P(z) = Σnj=0 ajzj with aj ≥ aj-1, a0 > 0 (j = 1, 2, ..., n), a classical result of Enestrom-Kakeya says that all the zeros of P(z) lie in |z| ≤ 1. This result was generalized by A. Joyal et al. [3] where they relaxed the non-negative condition on the coefficents. This result was further generalized by Dewan and Bidkham [9] by relaxing the monotonicity of the coefficients. In this paper, we use some techniques to obtain some more generalizations of the results [3], [8], [9].

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참고문헌

  1. M. Marden: Geometry of Polynomials. Amer. Math. Soc. Providence 40, 1949.
  2. W.M. Shah & A. Liman: On Enestrom-Kakeya theorem and related Analtyic Functions. Proc. Indian Acad. Sci (Math. Sci.) 117 (2007), no. 3, 359-370. https://doi.org/10.1007/s12044-007-0031-z
  3. A. Joyal, G. Labelle & Q.I. Rahman: On the Location of Zeros of Polynomials. Canad. Math. Bull. 10 (1967), no. 1, 53-60. https://doi.org/10.4153/CMB-1967-006-3
  4. A. Aziz & B.A. Zargar: Some Refinements of Enestrom-Kakeya theorem. Analysis in Theory and Applications 23 (2007), no. 2, 129-137. https://doi.org/10.1007/s10496-007-0129-2
  5. Q.I. Rahman & G. Schmeisser: Analytic Theory of the Polynomials. Oxford University Press 26, 2002.
  6. N.A. Rather, I. Dar & A. Iqbal: On the Regions containing all the Zeros of Polynomials and related Analytic Functions. Vestnik of St. Petersberg University. Mathematics. Mechanics. Astronomy 8 (2021), no. 2, 331-337. https://doi.org/10.21638/spbu01.2021.212
  7. A. Aziz & Q.G. Mohammad: Zero-free regions for Polynomials and some Generalizations of Enestrom-Kakeya theorem. Canad. Math. Bull. 27 (1984) 265-272. https://doi.org/10.4153/CMB-1984-040-3
  8. A. Aziz & B.A Zargar: Some extensions of Enestrom-Kakeya theorem. Glas, Mate. 31 (1996), 239-244.
  9. K.K. Dewan & M. Bidkham: On the Enestrom-Kakeya theorem. J. Math. Anal. Appl. 180 (1993), no. 1, 29-36. https://doi.org/10.1006/jmaa.1993.1379