International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 70192, 11 pages
Research Article

Construction of Planar Harmonic Functions

Jay M. Jahangiri,1 Herb Silverman,2 and Evelyn M. Silvia3

1Department of Mathematical Sciences, Kent State University, Burton 44021-9500, OH, USA
2Department of Mathematics, College of Charleston, Charleston 29424, SC, USA
3Department of Mathematics, University of California at Davis, Davis 95616-8633, CA, USA

Received 30 November 2006; Revised 4 February 2007; Accepted 6 February 2007

Academic Editor: Teodor Bulboaca

Dedicated to the memory of Evelyn Marie Silvia (1948–2006) Evelyn was a friend and colleague of Jay for 21 years and Herb for 37 years

Copyright © 2007 Jay M. Jahangiri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk can be written in the form f=h+g¯, where h and g are analytic in the open unit disk. The functions h and g are called the analytic and coanalytic parts of f, respectively. In this paper, we construct certain planar harmonic maps either by varying the coanalytic parts of harmonic functions that are known to be harmonic starlike or by adjoining analytic univalent functions with coanalytic parts that are related or derived from the analytic parts.