Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840191 | Nonlinear Analysis: Theory, Methods & Applications | 2013 | 10 Pages |
Abstract
In this paper we first determine conditions on the analytic polynomials pp and qq such that the family of univalent sense-preserving biharmonic polynomials of the form P=|z|2(p+q¯) is dense in the family of univalent sense-preserving biharmonic mappings FF defined on the unit disk DD of the form F=|z|2GF=|z|2G. Next, we consider the univalency of harmonic function GG whenever F=|z|2GF=|z|2G is univalent in DD. Finally, we give a partial answer to the problem raised by Muhanna about the radius of univalence of a family of sense-preserving biharmonic mappings with the form F=|z|2G+HF=|z|2G+H, where GG is univalent in DD.
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Authors
S. Ponnusamy, J. Qiao,