Journal Name:
- Mathematica Æterna
| Author Name | University of Author |
|---|---|
Abstract (2. Language):
Let H(D) be the linear space of all analytic functions de ned on
the open unit disc D = fz 2 C : jzj < 1g. A sense preserving loghar-
monic mapping is the solution of the non-linear elliptic partial di eran-
tial equation fz = w(z)fz( f
f ) where w(z) 2 H(D) is the second dilata-
tion of f such that jw(z)j < 1 for all z 2 D. It has been shown that
if f is a non-vanishing logharmonic mapping, then f can be expressed
as f(z) = h(z):g(z), where h(z) and g(z) are analytic in D with the
normalization h(0) 6= 0, g(0) = 1. If f vanishes at z = 0 but it is not
identically zero, then f admits the representation f = z: jzj2 h(z)g(z),
where Re >
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FULL TEXT (PDF):
- 8
669-674