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HOLOMORPHIC MAPPINGS INTO SOME DOMAIN IN A COMPLEX NORMED SPACE
Honda, Tatsuhiro Korean Mathematical Society 2004 대한수학회지 Vol.41 No.1
Let $D_1,\;D_2$ be convex domains in complex normed spaces $E_1,\;E_2$ respectively. When a mapping $f\;:\;D_1{\rightarrow}D_2$ is holomorphic with f(0) = 0, we obtain some results like the Schwarz lemma. Furthermore, we discuss a condition whereby f is linear or injective or isometry.
Holomorphic mappings into some domain in a complex normed space
Tatsuhiro Honda 대한수학회 2004 대한수학회지 Vol.41 No.1
Let D1,D2 be convex domains in complex normed spaces E1, E2 respectively. When a mapping f : D1 → D2 is holomorphic with f(0) = 0, we obtain some results like the Schwarz lemma. Furthermore, we discuss a condition whereby f is linear or injective or isometry.
QUASICONFORMAL EXTENSIONS OF STARLIKE HARMONIC MAPPINGS IN THE UNIT DISC
Hamada, Hidetaka,Honda, Tatsuhiro,Shon, Kwang Ho Korean Mathematical Society 2013 대한수학회보 Vol.50 No.4
Let $f$ be a harmonic mapping on the unit disc ${\Delta}$ in $\mathbb{C}$. We give some condition for $f$ to be a quasiconformal homeomorphism on ${\Delta}$ and to have a quasiconformal extension to the whole plane $\bar{\mathbb{C}}$. We also obtain quasiconformal extension results for starlike harmonic mappings of order ${\alpha}{\in}(0,1)$.
Quasiconformal extensions of starlike harmonic mappings in the unit disc
Hidetaka Hamada,손광호,Tatsuhiro Honda 대한수학회 2013 대한수학회보 Vol.50 No.4
Let f be a harmonic mapping on the unit disc Δ in C. We give some condition for f to be a quasiconformal homeomorphism on Δ and to have a quasiconformal extension to the whole plane C. We also obtain quasiconformal extension results for starlike harmonic mappings of order α∈2 (0, 1).