English

Harmonic Schwarzian derivative and methods of approximation of zeros

Complex Variables 2022-01-11 v1

Abstract

We review the relation between the classical formulas of the pre-Schwarzian and Schwarzian derivatives of locally univalent analytic functions and the derivatives of the generating functions of the methods due to Newton and Halley, respectively, for approximating zeros. We extend these relations to the cases when the functions considered are harmonic.

Keywords

Cite

@article{arxiv.2201.03009,
  title  = {Harmonic Schwarzian derivative and methods of approximation of zeros},
  author = {María J. Martín},
  journal= {arXiv preprint arXiv:2201.03009},
  year   = {2022}
}