A generalization of starlike functions
- 1 April 1990
- journal article
- research article
- Published by Taylor & Francis Ltd in Complex Variables and Elliptic Equations
- Vol. 14 (1-4), 77-84
- https://doi.org/10.1080/17476939008814407
Abstract
For every q. 0f, analytic on the open unit disc ℬ, f(0)=0, f′(0)=1 and |f(qz)| ⩽ |f(z)| on ℬ. This class is denoted by PSq . We study this class and explore the relationships between this class and other classes of analytic functions. We find the function F q that maximizes the coefficients of members of PS q. We also prove that a basic hypergeomelric function Ф(a,b;c;q,rz)ε PSq for certain values of r.Keywords
This publication has 2 references indexed in Scilit:
- Applications of Basic Hypergeometric FunctionsSIAM Review, 1974
- Starlike hypergeometric functionsProceedings of the American Mathematical Society, 1961