Extreme points method and univalent harmonic mappings

Authors

Yusuf Abu Muhanna, American University of Sharjah
Saminathan Ponnusamy, Indian Institute of Technology Madras

Document Type

Book Chapter

Publication Title

Contemporary Mathematics

Abstract

We consider the class of all sense-preserving complex-valued harmonic mappings f = h + g defined on the unit disk D with the normalization h(0) = h′ (0) − 1 = 0 and g(0) = g′ (0) = 0 with the second complex dilatation ω: D → D, g′ (z) = ω(z)h′ (z). In this paper, the authors determine sufficient conditions on h and ω that would imply the univalence of harmonic mappings f = h + g on D.

First Page

223

Last Page

237

DOI

10.1090/conm/667/13542

Publication Date

1-1-2016

Comments

Open Access; Green Open Access

Recommended Citation

Abu Muhanna, Yusuf and Ponnusamy, Saminathan, "Extreme points method and univalent harmonic mappings" (2016). Book Chapters. 234.
https://digitalcommons.isical.ac.in/book-chapters/234