Zeros of Lacunary Type of Polynomials
Abstract:
In this paper we use matrix methods and Gereshgorian disk Theorem to present some interesting generalizations of some well-known results concerning the distribution of the zeros of polynomial. Our results include as a special case some results due to A .Aziz and a result of Simon Reich-Lossar.
Author(s):
BA Zargar, Department of Mathematics University of Kashmir Srinagar
DOI:
Keywords:
References:
Alzer, H (1995). On the zeros of a Polynomial, J. Approx. Theory, 81, 421–424.
Aziz, A. Studies in zeros and Extremal properties of Polynomials, Ph.D. Thesis submitted to Kashmir University, 1981.
Bell, H.E (1965). Gereshgorian Theorem and the zero of polynomials, Amer. Math. Monthly, 72, 292–295.
Cauchy, A.L. Exercises de mathe’matique in ceurres 9(1929), 122.
Guggenheimmer, H (1964). On a note of Q.G. Mohammad, Amer. math. monthly, 71, 54–55.
Lossers, O.P (1971). Advanced problem 5739,Amer. Math. Monthly, 78, 681–683.
Mohammad, Q.G. (1965), On the zeros of polynomials, Amer. Math. Monthly, 72(6), 631–633.
Rahman, Q.I. (1970) A Bound for the moduli of the zeros of polynomials, Canad .math. Bull. 13, 541–542.
Rahman, Q.I. and Schmeisser, G. Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002.
Walsh, J.L (1924). An inequality for the roots of an algebraic equation. Ann.math. 25, 283–286.
