Bounds for the zeros of a quaternionic polynomial with restricted coefficients

The problem of determining the zeros of regular polynomials of a quaternionic variable with quaternionic coefficients is addressed in this study. We derive new bounds of the Enestrom-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our findings generalise several newly proven conclusions concerning the distribution of zeros of a quaternionic polynomial.

Keywords:

Quaternionic Polynomial , Zeros , Enestrom-Kakeya Theorem