IJPAM: Volume 69, No. 3 (2011)

ON A SUBCLASS OF HARMONIC UNIVALENT FUNCTIONS
DEFINED BY CONVOLUTION AND
INTEGRAL CONVOLUTION

K.K. Dixit$^1$, A.L. Pathak$^2$, S. Porwal$^3$, R. Agarwal$^4$
$^{1,3}$Department of Mathematics
Gwalior Institute of Information Technology
Gwalior, (M.P.) INDIA
$^3$e-mail: [email protected]
$^{2,4}$Department of Mathematics
Brahmanand College
The Mall, Kanpur, 208004, (U.P.) INDIA
$^2$e-mail: [email protected]
$^4$e-mail: [email protected]


Abstract. In this paper, we introduce and study a subclass of harmonic univalent functions defined by convolution and integral convolution. Coefficient bounds, extreme points, distortion bounds, convolution conditions and convex combination are determined for functions in this family. Consequently, many of our results are either extensions or new approaches to those corresponding to previously known results.

Received: January 3, 2011

AMS Subject Classification: 30C45, 30C50

Key Words and Phrases: harmonic function, analytic function, univalent function, starlike domain, convex domain, convolution

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 3