Growth of polynomials whose zeros are outside a circle

K. Dewan; Sunil Hans

Annales UMCS, Mathematica (2008)

  • Volume: 62, Issue: 1, page 61-65
  • ISSN: 2083-7402

Abstract

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If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that [...] In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.

How to cite

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K. Dewan, and Sunil Hans. "Growth of polynomials whose zeros are outside a circle." Annales UMCS, Mathematica 62.1 (2008): 61-65. <http://eudml.org/doc/267998>.

@article{K2008,
abstract = {If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that [...] In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.},
author = {K. Dewan, Sunil Hans},
journal = {Annales UMCS, Mathematica},
keywords = {Polynomials; inequalities; restricted zeros; growth; polynomials},
language = {eng},
number = {1},
pages = {61-65},
title = {Growth of polynomials whose zeros are outside a circle},
url = {http://eudml.org/doc/267998},
volume = {62},
year = {2008},
}

TY - JOUR
AU - K. Dewan
AU - Sunil Hans
TI - Growth of polynomials whose zeros are outside a circle
JO - Annales UMCS, Mathematica
PY - 2008
VL - 62
IS - 1
SP - 61
EP - 65
AB - If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that [...] In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.
LA - eng
KW - Polynomials; inequalities; restricted zeros; growth; polynomials
UR - http://eudml.org/doc/267998
ER -

References

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  1. Ankeny, N. C., Rivlin, T. J., On a theorem of S. Bernstein, Pacific J. Math. 5 (1955), 849-852. Zbl0067.01001
  2. Aziz, A., Growth of polynomials whose zeros are within or outside a circle, Bull. Austral. Math. Soc. 35 (1987), 247-256. Zbl0603.30003
  3. Govil, N. K., On a theorem of S. Bernstein, Proc. Nat. Acad. Sci. India Sect. A 50 (1980), 50-52. Zbl0493.30003
  4. Pólya, G., Szegö, G., Aufgaben und Lehrsatze aus der Analysis, Springer-Verlag, Berlin, 1925. Zbl51.0173.01

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