Zeros of a two-parameter family of harmonic quadrinomials

  • Oluma Ararso Alemu Addis Ababa University
  • Hunduma Legesse Geleta Addis Ababa University
Keywords: Analytic polynomials; harmonic polynomials; zero inclusion regions; quadrinomials

Abstract

In this paper, we determine the number of zeros and the zero inclusion regions of a two-parameter family of harmonic quadrinomials. We also determine a curve that separates sensepreserving and sense-reversing regions for these families of quadrinomials. Our work makes practical and effective use of the work of Wilmshurst, Khavinson, Dehmer, and also Bezout’s Theorem in the plane.

Author Biographies

Oluma Ararso Alemu, Addis Ababa University

Department of Mathematics,

Hunduma Legesse Geleta, Addis Ababa University

Department of Mathematics,

Published
2022-04-27
Section
Research articles

Journal Identifiers


eISSN: 2520-7997
print ISSN: 0379-2897