Object structure

Publication Details:

Established in 2008

Journal or Publication Title:

Armenian Journal of Mathematics=Հայկական մաթեմատիկական հանդես

Date of publication:

2025

Volume:

17

Number:

4

ISSN:

1829-1163

Official URL:


Title:

A Type of Eneström-Kakeya Theorem for Quaternionic Polynomials Involving Monotonicity with a Reversal

Creator:

Gardner, Robert B. ; Gladin, Matthew

Contributor(s):

Գլխ. խմբ.՝ Անրի Ներսեսյան ; Պատ. խմբ.՝ Լինդա Խաչատրյան ; Խմբ. տեղակալ՝ Ռաֆայել Բարխուդարյան

Subject:

Mathematics

Uncontrolled Keywords:

Location of Zeros of a Polynomial ; Quaternionic Polynomial ; Monotone Coefficients

Coverage:

1-10

Abstract:

The Eneström-Kakeya theorem states that if P ( z ) = ∑ n ℓ = 0 a ℓ z ℓ is a polynomial of degree n with real coefficients satisfying 0 ≤ a 0 ≤ a 1 ≤ ⋯ ≤ a n , then all zeros of P lie in | z | ≤ 1 in the complex plane. Motivated by recent results concerning an Eneström-Kakeya "type" condition on the real and imaginary parts of complex coefficients, we give similar results with hypotheses concerning the real and imaginary parts of the coefficients of a quaternionic polynomial. We give bounds on the moduli of quaternionic zeros of such polynomials.

Type:

Electronic journal

Format:

pdf

Identifier:

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General note:

Electronic Open Access Publication of the National Academy of Sciences of Armenia

Digitization:

ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան