Korean Journal of Mathematics

  • 제31권2호
  • /
  • Pages.153-160
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  • 2023
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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ON THE GROWTH OF POLYNOMIALS

  • Rubia Akhter (Department of Mathematics, Kashmir University) ;
  • B. A. Zargar (Department of Mathematics, Kashmir University) ;
  • M. H. Gulzar (Department of Mathematics, Kashmir University)
  • 투고 : 2022.12.27
  • 심사 : 2023.04.27
  • 발행 : 2023.06.30
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초록

In this paper, we study the growth of polynomials P(z) of degree n defined by $P(z)=z^s(a_0+\sum\limits_{j=t}^{n-s}a_jz^j)$, t ≥ 1, 0 ≤ s ≤ n-1 which do not vanish in the disk |z| ≤ k, k ≥ 1 except for the s-fold zeros at origin. Our result generalises and refines many results known in the literature.

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과제정보

The research is financially supported by NBHM, Government of India, under the research project 02011/36/2017/R&D-II.

참고문헌

  1. N. C. Ankeny and T. J. Rivilin, On a Theorem of S. Bernstein, Pacific J. Math. 5 (1955), 849-862. https://doi.org/10.2140/pjm.1955.5.849
  2. A. Dalal and N. K. Govil, On sharpening of a Theorem of Ankeny and Rivilin, Anal. Theory Appl. 36 (2018), 225-234.
  3. R. B. Gardner, N. K. Govil and S. R. Musukula, Rate of growth of polynomials not vanishing inside a circle, J. Ineq. Pure Appl. Math. 6 (2005), Art 53.
  4. R. B. Gardner, N. K. Govil and A. Weems, Growth of polynomial not vanishing inside a circle, Int. J. Pure Appl. Math., 13(2004), 487-494.
  5. N. K. Govil, On the maximum modulus of polynomials not vanishing inside the unit circle, Approx. Theory Appl. 5 (1989), 79-82. https://doi.org/10.1007/BF02836495
  6. N. K. Govil, On the growth of polynomials, J. Ineq. Appl. 7 (2002), 623-631.
  7. N. K. Govil, M. A. Qazi and Q. I. Rahman, Inequalities describing the growth of polynomialsnot vanishing in a disk of prescribed radius, Math. Inequal. Appl. 6 (2003), 491-498.
  8. E. Khojastehnezhad and M. Bidkham, Generalisation of some inequalities for the polar derivative of polynomials with restricted zeros, TWMS J. App. Eng. Math. 9 (2019), 485-492.
  9. M. Riesz, Uber einen Satz des Herrn Serge Bernstein, Acta. Math. 40 (1916), 337-347. https://doi.org/10.1007/BF02418550