Korean Journal of Mathematics

  • 제30권4호
  • /
  • Pages.615-628
  • /
  • 2022
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

SOME EXTENSIONS OF ENESTRÖM-KAKEYA THEOREM FOR QUATERNIONIC POLYNOMIALS

  • Shahbaz, Mir (Department of Mathematics, National Institute of Technology) ;
  • Abdul, Liman (Department of Mathematics, National Institute of Technology)
  • 투고 : 2022.08.10
  • 심사 : 2022.10.07
  • 발행 : 2022.12.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we will prove some extensions of the Eneström-Kakeya theorem to quaternionic polynomials which were already valid for the classical Eneström-Kakeya theorem to complex polynomials. Our kind of extensions have considerably improved the bounds by relaxing and weakening the hypothesis in some cases.

키워드

참고문헌

  1. Brand, L., The Roots of a Quaternion, Amer. Math. Monthly, 49 (8) (1942), 519-520.  https://doi.org/10.2307/2302858
  2. Carney, N.; Gardner, R.; Keaton, R. and Powers, A., The Eestrom-Kakeya theorem of a quarternionic variable, J. Appl.Theory, 250, Article 105325 (2020). 
  3. Dinesh, D., A note on Enestrom-Kakeya theorem for a polynomial with quaternionic variable, Arab. J. Math. 9 (2020), 707-714.  https://doi.org/10.1007/s40065-020-00283-0
  4. Enestrom, G., Remarque sur un theoreme relatif aux racines de 1' equation anxn + ... + a0 = 0 ou tous les coefficientes a sont reels et positifs, Tohoku Math. J. 18 (1920), 34-36. 
  5. Gauss, C.F.,Beitrage Zur Theorie der algebraischen Gleichungen,Abh.Ges.Wiss.Gottingen, 4 (1850), 73-102. 
  6. Gentili, G.; Stoppato, C., Zeros of regular functions and polynomials of a quaternionic variable, Michigan Math. J. 56 (2008), 655-667.  https://doi.org/10.1307/mmj/1231770366
  7. Gentili, G.; Struppa, D. A new theory of regular functions of a quaternionic variable, Adv. Math. 216 (2007), 279-301.  https://doi.org/10.1016/j.aim.2007.05.010
  8. Govil, N.K.; Rahman, Q.I., On the Enestrom-Kakeya theorem, Tohoku Math. J. 20 (2) (1968), 126-136.  https://doi.org/10.2748/tmj/1178243172
  9. Hurwitz, A., Uber einen Satz des Harrn Kakeya, Tohoku Math. J. First Ser. 4 (1913-1914), 626-631. 
  10. Joyal, A.; Labelle, G.; Rahman, Q.I., On the location of zeros of polynomials., Can. Math. Bull. 10 (1) (1967), 53-63.  https://doi.org/10.4153/CMB-1967-006-3
  11. Kakeya, S., On the limits of the roots of an algebraic equation with positive coefficient, Tohoku Math. J. 2 (1912-1913), 140-142. 
  12. Liman, A., Hussain, S., Hussain, I., A Note on a Generalisation of Enestrom-Kakeya Theorem for Quaternionic Polynomials. Mediterranean Journal of Mathematics 19 (4) (2022), 1-10.  https://doi.org/10.1007/s00009-021-01753-1
  13. Marden, M., Geometry of Polynomials., Math. Surveys, No. 3, Amer. Math. Soc.