Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings
2009 ◽
Vol 2009
◽
pp. 1-14
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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2014 ◽
Vol 98
(2)
◽
pp. 257-280
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1988 ◽
Vol 103
(3)
◽
pp. 487-495
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