On maximum modulus for the derivative of a polynomial

K. Dewan; Sunil Hans

Annales UMCS, Mathematica (2009)

  • Volume: 63, Issue: 1, page 55-62
  • ISSN: 2083-7402

Abstract

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If P(z) is a polynomial of degree n, having all its zeros in the disk [...] then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] that [...] In this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type [...] Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.

How to cite

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K. Dewan, and Sunil Hans. "On maximum modulus for the derivative of a polynomial." Annales UMCS, Mathematica 63.1 (2009): 55-62. <http://eudml.org/doc/268104>.

@article{K2009,
abstract = {If P(z) is a polynomial of degree n, having all its zeros in the disk [...] then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] that [...] In this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type [...] Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.},
author = {K. Dewan, Sunil Hans},
journal = {Annales UMCS, Mathematica},
keywords = {Polynomials; inequalities; derivatives; zeros; polynomials},
language = {eng},
number = {1},
pages = {55-62},
title = {On maximum modulus for the derivative of a polynomial},
url = {http://eudml.org/doc/268104},
volume = {63},
year = {2009},
}

TY - JOUR
AU - K. Dewan
AU - Sunil Hans
TI - On maximum modulus for the derivative of a polynomial
JO - Annales UMCS, Mathematica
PY - 2009
VL - 63
IS - 1
SP - 55
EP - 62
AB - If P(z) is a polynomial of degree n, having all its zeros in the disk [...] then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] that [...] In this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type [...] Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.
LA - eng
KW - Polynomials; inequalities; derivatives; zeros; polynomials
UR - http://eudml.org/doc/268104
ER -

References

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  1. Bernstein, S., Lecons sur les propriétés extrémales et la meilleure approximation desfonctions analytiques d'une variable réelle, Gauthier Villars, Paris, 1926. Zbl52.0256.02
  2. Dewan, K. K., Mir, A., Note on a theorem of S. Bernstein, Southeast Asian Bull. Math. 31 (2007), 691-695. Zbl1150.30001
  3. Govil, N. K., On the derivatives of a polynomial, Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546. Zbl0279.30004
  4. Govil, N. K., On a theorem of S. Bernstein, J. Math. Phys. Sci., 14, no. 2 (1980), 183-187. Zbl0444.30007
  5. Govil, N. K., Some inequalities for derivatives of polynomials, J. Approx. Theory 66 (1991), 29-35. Zbl0735.41006
  6. 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. Zbl0189.08502
  7. Pólya, G., Szegö, G., Problems and Theorems in Analysis, Vol. 1, Springer-Verlag, New York, 1972. Zbl0236.00003
  8. Qazi, M. A., On the maximum modulus of polynomials, Proc. Amer. Math. Soc. 115 (1992), 337-343. Zbl0772.30006
  9. Turán, P., Über die ableitung von Polynomen, Compositio Math. 7 (1939), 89-95. Zbl65.0324.01

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