Inequalities concerning polar derivative of polynomials

• Autorzy: Arty Ahuja , K. K. Dewan , Sunil Hans
• Języki publikacji: EN

Abstrakty

EN

In this paper we obtain certain results for the polar derivative of a polynomial \(p(z) = c_nz^n +\sum_{j=\mu}^n c_{n-j}z^{n-j}\), \(1\leq\mu\leq n\), having all its zeros on \(|z| = k\), \(k\leq 1\), which generalizes the results due to Dewan and Mir, Dewan and Hans. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros. [Editor's note: There are flaws in the paper, see M. A. Qazi, Remarks on some recent results about polynomials with restricted zeros, Ann. Univ. Mariae Curie-Skłodowska Sect. A 67 (2), (2013), 59-64 ]

Słowa kluczowe

EN

Polynomials; maximum modulus; inequalities in the complex domain; polar derivative

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2011
• Tom: 65
• Numer: 1

Daty

wydano

2011

online

2016-07-25

Twórcy

autor

Arty Ahuja

autor

K. K. Dewan

autor

Sunil Hans

Bibliografia

• Bernstein, S., Lecons sur les proprietes extremales et la meilleure approximation desfonctions analytiques d’une variable reele, Gauthier Villars, Paris, 1926 (French).
• Chan, T. N., Malik, M. A., On Erdos-Lax theorem, Proc. Indian Acad. Sci. 92 (3) (1983), 191-193.
• Dewan, K. K., Hans, S., On maximum modulus for the derivative of a polynomial, Ann. Univ. Mariae Curie-Skłodowska Sect. A 63 (2009), 55-62.
• Dewan, K. K., Mir, A., Note on a theorem of S. Bernstein, Southeast Asian Bulletin of Math. 31 (2007), 691-695.
• Govil, N. K., On the theorem of S. Bernstein, J. Math. Phys. Sci. 14 (1980), 183-187.
• Govil, N. K., Rahman, Q. I., Functions of exponential type not vanishing in a half plane and related polynomials, Trans. Amer. Math. Soc. 137 (1969), 501-517.
• Jain, V. K., On polynomials having zeros in closed exterior or interior of a circle, Indian J. Pure Appl. Math. 30 (1999), 153-159.
• Malik, M. A., On the derivative of a polynomial, J. London Math. Soc. 1 (1969), 57-60.
• Mir, A., On extremal properties and location of zeros of polynomials, Ph.D. Thesis submitted to Jamia Millia Islamia, New Delhi, 2002.
• Qazi, M. A., On the maximum modulus of polynomials, Proc. Amer. Math. Soc. 115 (1992), 337-343.

Identyfikatory

DOI

10.17951/a.2011.65.1.1-9