Harmonic univalent functions with fixed second ... - Project Euclid
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Harmonic univalent functions with fixed second ... - Project Euclid
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Hokkaido Mathematical Journal Vol. 31 (2002) p.
431-439
Harmonic univalent functions with fixed second coefficient Om P. AHUJA and Jay M. JAHANGIRI (Received February 5, 2001) Abstract. We define and investigate a family of harmonic univalent functions that have fixed second coefficient. Extreme points, convolution conditions, convex combinations, and distortion bounds are obtained for these functions.
Key words: harmonic, univalent, starlike, convex.
1.
Introduction
Denote by H the family of functions f=h+\overline{g} which are harmonic univalent and sense-preserving in the open unit disk \triangle=\{z : |z|
