On a class of meromorphic starlike functions with positive coeffients

Year 1994, Volume: 43 , 0 - 0, 01.01.1994

Kumar Pal Shıv

https://doi.org/10.1501/Commua1_0000000475

Abstract

Let T„(A, B, Zq) denote tlıe class of functions f (z) — a z
+
ce
S a„z“ (a > I, aiı > 0) regular and univalent in the disc ü'
n=ı
{z: 0 İz I 1 {, satisfying 1 -|- Aw (z) 1 -j- Bav (z)
f^z) f(z)
— z , for z e U', and
AV e E (Avhere E is the class of analytic functions av Avith Av(0)= 0 and I AV (z) I < 1), Avhere -1 ; A < B < 1, 0 < B <1 andf' (zq) I
z^o (0 ^0 1). In this paper, sharp coefficient eştimates for the çlass Tjj (A, B, zo) have been studied Radius of meromorphic conyexity, integral transform of functions in Tjj (A, B, Zq) have been obtained.
It is also provpd tliat the class Tjj (A, B, Zq) is closed under convex linear combination. In the last part, the convolution problem of these functions have been ştudied.

Keywords

meromorphic starlike, positive coeffients, Statistics

References

• Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi