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On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem

Abdullah Mir (2023)

Czechoslovak Mathematical Journal

We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.

On the zeros of polynomials and analytic functions

Roshan Lal, Susheel Kumar, Sunil Hans (2011)

Annales UMCS, Mathematica

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.

On two new functional equations for generalized Joukowski transformations

M. Baran, H. Haruki (1991)

Annales Polonici Mathematici

The purpose of this paper is to solve two functional equations for generalized Joukowski transformations and to give a geometric interpretation to one of them. Here the Joukowski transformation means the function 1 / 2 ( z + z - 1 ) of a complex variable z.

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