On the coefficient conjecture of Clunie and Sheil-Small on Univalent Harmonic Mappings
Complex Variables
2014-03-25 v1
Abstract
In this paper, we first prove the coefficient conjecture of Clunie and Sheil-Small for a class of univalent harmonic functions which includes functions convex in some direction. Next, we prove growth and covering theorems and some related results. Finally, we propose two conjectures. An affirmative answer to one of which would then imply for example a solution to the conjecture of Clunie and Sheil-Small.
Keywords
Cite
@article{arxiv.1403.5619,
title = {On the coefficient conjecture of Clunie and Sheil-Small on Univalent Harmonic Mappings},
author = {S. Ponnusamy and A. Sairam Kaliraj},
journal= {arXiv preprint arXiv:1403.5619},
year = {2014}
}
Comments
14 pages, 10 figures; article is with a journal