• Korean Journal of Mathematics
• /
• v.30 no.3
• /
• pp.503-512
• /
• 2022

In this paper, we are concerned with the problem of locating the zeros of regular polynomials of a quaternionic variable with quaternionic coefficients. 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 in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results generalize some recently proved results about the distribution of zeros of a quaternionic polynomial.

• Korean Journal of Mathematics
• /
• v.30 no.4
• /
• pp.615-628
• /
• 2022

In this paper, we will prove some extensions of the Eneström-Kakeya theorem to quaternionic polynomials which were already valid for the classical Eneström-Kakeya theorem to complex polynomials. Our kind of extensions have considerably improved the bounds by relaxing and weakening the hypothesis in some cases.