Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings
We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. The regions (their bo...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2009-01-01
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Series: | International Journal of Mathematics and Mathematical Sciences |
Online Access: | http://dx.doi.org/10.1155/2009/834215 |
Summary: | We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. The regions (their boundaries) are determined explicitly and the proofs rely on Schwarz lemma or subordination. |
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ISSN: | 0161-1712 1687-0425 |