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

Received: 18 January 2014/Accepted: 15 March 2014

ABSTRACT

Let A denote the class of functions f that are analytic in the unit disc D and normalized by f (0) = f ʹ(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

REFERENCES

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*Corresponding author; email: jsokol@prz.edu.pl