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

Diserahkan: 17 Disember 2013/Diterima: 8 Julai 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

RUJUKAN

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*Pengarang untuk surat-menyurat; email: ykahramaner@ticaret.edu.tr