Sains Malaysiana 44(1)(2015): 155–158
On
Starlikeness of Libera Transform
(Jelmaan Libera Seperti Bintang)
MAMORU NUNOKAWA1 & JANUSZ SOKÓŁ2*
1University
of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba 260-0808, Japan
2Department
of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy
12,
35-959 RzeszówPoland
Diserahkan: 18 Januari 2014/Diterima:
15 Mac 2014
ABSTRACT
Let A denote the
class of functions f that are analytic in the unit disc D and normalized
by f (0) = f'
(0) –
1 = 0. In this paper conditions are determined for starlikeness
of the Libera integral of functions such that ⎪arg {f ʹ}⎪ < δ in D. The results of Miller and
Mocanu (2002) on Libera transform of functions with bounded turning
are improved.
Keywords: Nunokawa's lemma; starlike
functions; strongly starlike functions
ABSTRAK
Biarkan
A
menandakan kelas fungsi f yang analitik dalam cakera unit D dan dinormalkan oleh
f (0) = f'
(0) –
1 = 0. Dalam kertas ini keadaan ditentukan
untuk fungsi kamiran Libera seperti bintang adalah ⎪arg {f ʹ}⎪ < δ dalam D . Keputusan Miller dan Mocanu (2002)
atas transformasi fungsi Libera dengan pusingan terbatas bertambah
baik.
Kata kunci: Fungsi seperti
bintang; fungsi seperti bintang yang kuat; lema Nunokawa
RUJUKAN
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1993. On the order of strongly starlikeness of strongly convex
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Sokół,
J. 2008. Starlikeness of the Libera transform of functions with bounded
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Stankiewicz,
J. 1966. Quelques probl`emes extremaux dans les classes des fonctions
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*Pengarang
untuk surat-menyurat; email: jsokol@prz.edu.pl
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