ArticleOriginal scientific text
Title
Starlikeness of functions satisfying a differential inequality
Authors 1, 2, 3
Affiliations
- School of Mathematics, Spic Science Foundation, 92 G.N. Chetty Road, Madras 600 017, India
- 3A/95 Azad Nagar, Kanpur 208002, India
- School of Mathematical and Computer Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
Abstract
In a recent paper Fournier and Ruscheweyh established a theorem related to a certain functional. We extend their result differently, and then use it to obtain a precise upper bound on α so that for f analytic in |z| < 1, f(0) = f'(0) - 1 = 0 and satisfying Re{zf''(z)} > -λ, the function f is starlike.
Keywords
univalent, convex, starlike, close-to-convex functions, duality of Hadamard products
Bibliography
- R. Fournier and S. Ruscheweyh, On two extremal problems related to univalent functions, Rocky Mountain J. Math. 24 (1994), 529-538.
- S. Ruscheweyh, Duality for Hadamard products with applications to extremal problems for functions regular in the unit disc, Trans. Amer. Math. Soc. 210 (1975), 63-74.
- S. Ruscheweyh, Convolution in Geometric Function Theory, Les Presses de l'Université de Montréal, Montréal, 1982.
Pages:
135-140
Main language of publication
English
Received
1993-10-12
Accepted
1994-04-10
Published
1995
Exact and natural sciences