For a polynomial of degree n, we have obtained some results, which generalize and improve upon the earlier well known results (under certain conditions). A similar result is also obtained for analytic function.
@article{bwmeta1.element.doi-10_2478_v10062-011-0008-3,
author = {Roshan Lal and Susheel Kumar and Sunil Hans},
title = {On the zeros of polynomials and analytic functions},
journal = {Annales UMCS, Mathematica},
volume = {65},
year = {2011},
pages = {97-108},
zbl = {1253.30018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-011-0008-3}
}
Roshan Lal; Susheel Kumar; Sunil Hans. On the zeros of polynomials and analytic functions. Annales UMCS, Mathematica, Tome 65 (2011) pp. 97-108. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-011-0008-3/
Gardner, R. B., Govil, N. K., Some generalizations of the Eneström-Kakeya theorem, Acta Math. Hungar. 74 (1-2) (1997), 125-134. | Zbl 0926.30005
Govil, N. K., Rahman, Q. I., On the Eneström-Kakeya theorem, Tôhoku Math. J. 20 (1968), 126-136.[Crossref] | Zbl 0194.10201
Jain, V. K., On the zeros of a polynomial, Proc. Indian Acad. Sci. Math. Sci. 119 (1) (2009), 37-43. | Zbl 1173.30005
Joyal, A., Labelle, G. and Rahman, Q. I., On the location of zeros of polynomials, Canadian Math. Bull. 10 (1967), 55-63. | Zbl 0152.06102
Marden, M., The Geometry of Polynomials, Math. Surveys No. 3, Amer. Math. Soc., Providence, RI, 1966. | Zbl 0162.37101
Pellet, M.A., Sur un mode de séparation des racines des équations et la formule de Lagrange, Bull. Sci. Math. 5 (1881), 393-395. | Zbl 13.0074.01