Inequalities concerning polar derivative of polynomials
Arty Ahuja; K. K. Dewan; Sunil Hans
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2011)
- Volume: 65, Issue: 1
- ISSN: 0365-1029
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topArty Ahuja, K. K. Dewan, and Sunil Hans. "Inequalities concerning polar derivative of polynomials." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 65.1 (2011): null. <http://eudml.org/doc/289768>.
@article{ArtyAhuja2011,
abstract = {In this paper we obtain certain results for the polar derivative of a polynomial $p(z) = c_nz^n +\sum _\{j=\mu \}^n c_\{n-j\}z^\{n-j\}$, $1\le \mu \le n$, having all its zeros on $|z| = k$, $k\le 1$, 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 ]},
author = {Arty Ahuja, K. K. Dewan, Sunil Hans},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Polynomials; maximum modulus; inequalities in the complex domain; polar derivative},
language = {eng},
number = {1},
pages = {null},
title = {Inequalities concerning polar derivative of polynomials},
url = {http://eudml.org/doc/289768},
volume = {65},
year = {2011},
}
TY - JOUR
AU - Arty Ahuja
AU - K. K. Dewan
AU - Sunil Hans
TI - Inequalities concerning polar derivative of polynomials
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2011
VL - 65
IS - 1
SP - null
AB - In this paper we obtain certain results for the polar derivative of a polynomial $p(z) = c_nz^n +\sum _{j=\mu }^n c_{n-j}z^{n-j}$, $1\le \mu \le n$, having all its zeros on $|z| = k$, $k\le 1$, 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 ]
LA - eng
KW - Polynomials; maximum modulus; inequalities in the complex domain; polar derivative
UR - http://eudml.org/doc/289768
ER -
References
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- 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.
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