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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