English

Note on the Coefficient Conjecture of Clunie and Sheil-Small on the univalent harmonic mapping

Complex Variables 2026-02-17 v1

Abstract

In this article, we construct generalized harmonic univalent mappings and find its coefficients bounds. We present the counterexample to validate the coefficient conjecture proposed by Clunie and Sheil-Small for the class of functions f=h+gSHf=h+\overline{g}\in \mathcal{S}_{\mathcal{H}} with the help of these examples we improve the conjecture bounds of class SH\mathcal{S}_{\mathcal{H}}.

Keywords

Cite

@article{arxiv.2602.13613,
  title  = {Note on the Coefficient Conjecture of Clunie and Sheil-Small on the univalent harmonic mapping},
  author = {Omendra Mishra and Asena Çetinkaya},
  journal= {arXiv preprint arXiv:2602.13613},
  year   = {2026}
}