IJPAM: Volume 63, No. 2 (2010)

ON A CLASS OF HARMONIC UNIVALENT
FUNCTIONS DEFINED BY A LINEAR OPERATOR

Pravati Sahoo$^1$, Saumya Singh$^2$
$^{1,2}$Department of Mathematics
Banaras Hindu University (BHU)
Banaras, Varanasi, 221 005, INDIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.Let $S_H$ denote the class of functions $f=h+\bar{g}$ which are harmonic, univalent and sense preserving in the unit disc $\Delta$. We define a new subclass $SHL(\alpha, \beta)$ by using a linear operator of harmonic univalent functions. In this paper, coefficient bounds, distortion bounds and extreme points are obtained.

Received: July 20, 2010

AMS Subject Classification: 30C45, 30C50, 31C05

Key Words and Phrases: harmonic functions, harmonic starlike function, linear operator, distortion bounds

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 2