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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 71 Issue: 3

On the maximum modulus of a complex polynomial

Shabir Malik(University of Kashmir, Jammu and Kashmir, India)0000-0002-6906-6513
Ashish Kumar(University of Kashmir)0000-0002-7423-4403
Sayfa
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Yayın Tarihi
2022-09-30
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Moreover, the problem of estimating p ( 1 − w n ) p(1−wn) , $0<w\leq$ given $p(1)=0$ is considered.

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Amaç & Hipotez:In this paper we impose distinct restrictions on the moduli of the zeros of p ( z ) = n ∑ v = 0 a v z v p(z)=∑v=0navzv and investigate the dependence of ∥ p ( R z ) − p ( σ z ) ∥ ‖p(Rz)−p(σz)‖ , R > σ ≥ 1 R>σ≥1 on M α Mα and M α + π Mα+π , where M α = max 1 ≤ k ≤ n | p ( e i ( α + 2 k π ) / n ) | Mα=max1≤k≤n|p(ei(α+2kπ)/n)| and on certain coefficients of p ( z ) p(z) .
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Temel Bulgular & Veri:This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases.
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Sonuç & Katkı:Moreover, the problem of estimating p ( 1 − w n ) p(1−wn) , $0<w\leq$ given $p(1)=0$ is considered.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Polynomials · definite integral · zeros

Abstract

In this paper we impose distinct restrictions on the moduli of the zeros of p ( z ) = n ∑ v = 0 a v z v p(z)=∑v=0navzv and investigate the dependence of ∥ p ( R z ) − p ( σ z ) ∥ ‖p(Rz)−p(σz)‖ , R > σ ≥ 1 R>σ≥1 on M α Mα and M α + π Mα+π , where M α = max 1 ≤ k ≤ n | p ( e i ( α + 2 k π ) / n ) | Mα=max1≤k≤n|p(ei(α+2kπ)/n)| and on certain coefficients of p ( z ) p(z) . This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases. Moreover, the problem of estimating p ( 1 − w n ) p(1−wn) , $0<w\leq$ given $p(1)=0$ is considered.

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Bu Makaleye Atıf Yap

Malik, S., Kumar, A. (2022). On the maximum modulus of a complex polynomial. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 71 Issue: 3. https://doi.org/10.31801/cfsuasmas.989344

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Kaynakça (15)

  1. Ahmad, I., Some generalizations of Bernstein type inequalities, Int. J. Modern Math. Sci., 4(3) (2012), 133-138.
  2. Aziz, A., A refinement of an inequality of S. Bernstein, J. Math. Anal. Appl., 144 (1989), 226-235. https://doi.org/10.1016/0022-247X(89)90370-3
  3. Aziz, A., Rather, N. A., New $L^q$ inequalities for polynomials, Mathematical Inequalities and Applications, 2 (1998), 177-191.
  4. Bernstein, S.N., EMales Et La Meilleure Approximation Des Fonctions Analytiques D’une Variable REElle, Gauthier-Villars, Paris, 1926.
  5. Dewan, K. K., Kaur, J., Mir, A., Inequalities for the derivative of a polynomial, J. Math. Anal. Appl., 269 (2002), 489-499. https://doi.org/10.1016/S0022-247X(02)00030-6
  6. Frappier, C., Rahman, Q. I., Ruscheweyh, St., New inequalities for polynomials, Trans. Amer. Math. Soc., 288 (1985), 69-99. https://doi.org/10.2307/2000427
  7. Gulzar, M. H., Inequalities for a polynomial and its derivative, International Journal of Mathematical Archive, 3(2) (2012), 528-533.
  8. Lax, P. D., Proof of a conjecture of P. Erdos on the derivatives of a polynomial, Bull. Amer. Math. Soc., 50 (1944), 509-513.
  9. Marden, M., Geometry of Polynomials, Second Edition, Mathematical Surveys, Amer. Math. Soc. Providence R.I. 1996.
  10. Milovanovic, G. V., Mitrinovi´c, D. S., Rassias, Th.M., Topics in Polynomials Extremal Problems, Inequalities, Zeros, World Scientific, Singapore, 1994.
  11. Polya, G., Szego, G., Aufgaben und Lehrsatze aus der Analysis, Springer, Berlin, 1925.
  12. Rahman, Q. I., Schmeisser, G., Analytic Theory of Polynomials, Oxford University Press, New York, 2002.
  13. Rather, N. A., Shah, M. A., On the derivative of a polynomial, Applied Mathematics, 3 (2012), 746-749. http://dx.doi.org/10.4236/am.2012.37110
  14. Riesz, M., Eine trigonometrische interpolation formel und einige Ungleichung fur Polynome, Jahresber. Dtsch. Math.Verein, 23 (1914), 354-368.
  15. Riesz, M., Über einen Sat’z des Herrn Serge Bernstein, Acta Math., 40 (1916), 337-347.