Bounds for the Zeros of a Quaternionic Polynomial with Restricted Coefficients

In this paper, we are concerned with the problem of locating the zeros of polynomials and regular functions with quaternionic coefficients when their real and imaginary parts are restricted. The extended Schwarz’s lemma, the maximum modulus theorem, and the structure of the zero sets defined in the newly constructed theory of regular functions and polynomials of a quaternionic variable are used to deduce the bounds for the zeros of these polynomials and regular functions. Our findings generalise certain recently established results about the zero distribution for this subclass of regular functions.