Some Bounds for Zeros of a Polynomial with Restricted coefficients

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2024, v.31 no.1, pp.49-56

https://doi.org/10.7468/jksmeb.2024.31.1.49

Mahnaz Shafi Chishti (Shobhit Institute of Engineering & Technology(Deemed to be University) Meerut)
Vipin Kumar Tyagi (Shobhit Institute of Engineering and Technology(Deemed to be University) Meerut)
Mohammad Ibrahim Mir (University of Kashmir)

Mahnaz, S. C. , Vipin, K. T. , & Mohammad, I. M. (2024). . 한국수학교육학회지시리즈B:순수및응용수학, 31(1), 49-56, https://doi.org/10.7468/jksmeb.2024.31.1.49

복사

Abstract

For a Polynomial P(z)= SMALLSUM _{j=0}^{n} `a _{j} z ^{j} with a_j ≥ a_j−1, a_0 > 0 (j = 1, 2, ..., n), a classical result of Enestrom-Kakeya says that all the zeros of P(z) lie in |z| ≤ 1. This result was generalized by A. Joyal et al. [3] where they relaxed the non-negative condition on the coefficents. This result was further generalized by Dewan and Bidkham [9] by relaxing the monotonicity of the coefficients. In this paper, we use some techniques to obtain some more generalizations of the results [3], [8], [9].

keywords: bound, coefficient, polynomial, zeros.

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논문 상세

Vol.31 No.1

Some Bounds for Zeros of a Polynomial with Restricted coefficients

Abstract

한국수학교육학회지시리즈B:순수및응용수학