Note on the Coefficient Conjecture of Clunie and Sheil-Small on the univalent harmonic mapping
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 $f=h+\overline{g}\in \mathcal{S}_{\mathcal{H}}$ with the help of these examples we improve the conjecture bounds of class $\mathcal{S}_{\mathcal{H}}$.
Fields of Study & Subjects
Analytic and geometric function theory
Holomorphic and Operator Theory
Mathematical Inequalities and Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 14 February 2026
- Language
- EN
- Document type
- Preprint