منابع مشابه
On the Location of Zeros of Polynomials
then P z has all the zeros in z t . In the literature, [1-15], there exist extensions and generalizations of Eneström-Kakeya theorem. Joyal, Labelle and Rahman [9] extended this theorem to polynomials whose coefficients are monotonic but not necessarily non negative and the result was further generalized by Dewan and Bidkham [6] to read as: Theorem B. If =0 := n j j j P z a z is a p...
متن کاملLocation of Zeros of Wiener and Distance Polynomials
The geometry of polynomials explores geometrical relationships between the zeros and the coefficients of a polynomial. A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated. In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely ...
متن کاملOn the Location of Zeros of Complex Polynomials
This paper proves bounds for the zeros of complex valued polynomials. The assertions stated in this work have been specialized in the area of the location of zeros for complex polynomials in terms of two foci: (i) finding bounds for complex valued polynomials with special conditions for the coefficients and (ii) locating zeros of complex valued polynomials without special conditions for the coe...
متن کاملSome compact generalization of inequalities for polynomials with prescribed zeros
Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$. In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$, $k^2 leq rRleq R^2$ and for $Rleq r leq k$. Our results refine and generalize certain well-known polynomial inequalities.
متن کاملOn the Location of the Zeros of Certain Polynomials
Abstract. We extend Aziz and Mohammad’s result that the zeros, of a polynomial P (z) = ∑n j=0 ajz , taj > aj−1 > 0, j = 2, 3, . . . , n for certain t ( > 0), with moduli greater than t(n − 1)/n are simple, to polynomials with complex coefficients. Then we improve their result that the polynomial P (z), of degree n, with complex coefficients, does not vanish in the disc |z − ae| < a/(2n); a > 0,...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2009
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2009.02.001