ArticleOriginal scientific text
Title
On coefficient inequalities in the Carathéodory class of functions
Authors 1
Affiliations
- Department of Mathematics, Technical University of Rzeszów, W. Pola 2, 35-959 Rzeszów, Poland
Abstract
Some inequalities are proved for coefficients of functions in the class P(α), where α ∈ [0,1), of functions with real part greater than α. In particular, new inequalities for coefficients in the Carathéodory class P(0) are given.
Keywords
Carathéodory class, coefficient inequalities
Bibliography
- C. Carathéodory, Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann. 64 (1907), 95-115.
- A. W. Goodman, Univalent Functions, Mariner, Tampa, FL 1983.
- Z. J. Jakubowski and J. Stankiewicz, On some classes of functions with the special normalizations, Folia Sci. Univ. Tech. Res. 73 (1990), 29-48.
- M. S. Robertson, On the theory of univalent functions, Ann. of Math. 37 (1936), 374-408.
- M. S. Robertson, Univalent functions starlike with respect to a boundary point, J. Math. Anal. Appl. 81 (1981), 327-345.
Pages:
59-67
Main language of publication
English
Received
1999-09-27
Accepted
2000-02-21
Published
2000
Exact and natural sciences