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Sains Malaysiana 43(12)(2014):
1961–1964
Quasiconformal Harmonic Mappings Related to Janowski Starlike Functions (Pemetaan Harmonik Kuasimensebentuk Berkaitan dengan Fungsi
Bakbintang Janowski)
YASEMIN KAHRAMANER1*
& YAŞAR POLATOĞLU2
1Department of Mathematics,
Istanbul Commerce University, İstanbul, Turkey
2Department of
Mathematics and Computer Science, İstanbul Kültür Üniversitesi,
İstanbul
Turkey
Received: 17 December 2013/Accepted: 8 July 2014
ABSTRACT
Let be a univalent sense-preserving harmonic mapping of the open
unit disc D = {z⎜ ⎜z⎜ < 1}. If f
satisfies the condition ⎜ω(z)⎜= < k, 0 < k < 1, then
is called k-quasiconformal harmonic mapping in D. The main purpose of this
paper was to give some properties of the class of k-quasiconformal mappings
related to Janowski starlike functions.
Keywords: Coefficient inequality; distortion theorem; growth
theorem; k-quasiconformal mapping
ABSTRAK
Andaikan pemetaan harmonik terawet univalen bagi cakera unit
terbuka D = {z⎜ ⎜z⎜ < 1}. Jika f
memenuhi syarat ⎜ω(z)⎜= < k, 0 < k < 1, maka f dipanggil pemetaan harmonik k-kuasimensebentuk dalam D.
Tujuan utama kertas ini adalah untuk memberi beberapa sifat bagi kelas pemetaan
k-kuasimensebentuk yang berkaitan dengan fungsi bakbintang Janowski.
Kata kunci: Ketaksamaan pekali; pemetaan
k-kuasimensebentuk; teorem erotan; teorem pertumbuhan
REFERENCES
Clunie, J. 1959. On Meromorphic schlicht
functions. J. London Math. Soc. 34: 215-216.
Duren, P. 2004. Harmonic Mappings in
the Plane. Vol. 156 of Cambridge Tracts in Mathematics. Cambridge:
Cambridge University Press.
Duren, P. 1983. Univalent Functions. Berlin: Springer
Verlag.
Goodman, A.W. 1983. Univalent Functions. Volume I.
Tampa Florida: Mariner Publishing Company Inc.
Jack, I.S. 1971. Functions starlike and convex of order
alpha. J. London Math. Soc. 3: 369-374.
Janowski, W. 1973. Some extremal problems for certain families of analytic
functions I. Annales Policini Mathematici 28: 297-326.
Lewys, H. 1936. On the non-vanishing of
the Jacobian in certain one-to-one mappings. Bull. Amer. Math. Soc.
42: 689-692.
*Corresponding author; email: ykahramaner@ticaret.edu.tr
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