Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 14, Number 4 (2010), 1479-1490.
CLASSES OF MEROMORPHIC α-CONVEX FUNCTIONS
For a fixed analytic univalent function $\phi$, the class of meromorphic univalent $\alpha$-convex functions with respect to $\phi$ is introduced. A representation theorem for functions in the class, as well as a necessary and sufficient condition for functions to belong to the class are obtained. Also we obtain a sharp growth theorem and estimate on a certain coefficient functional for meromorphic starlike functions with respect to $\phi$. Differential subordination and superordination conditions are also obtained for the subclass of meromorphic starlike functions with respect to $\phi$.
Taiwanese J. Math., Volume 14, Number 4 (2010), 1479-1490.
First available in Project Euclid: 18 July 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination
Ali, Rosihan M.; Ravichandran, V. CLASSES OF MEROMORPHIC α-CONVEX FUNCTIONS. Taiwanese J. Math. 14 (2010), no. 4, 1479--1490. doi:10.11650/twjm/1500405962. https://projecteuclid.org/euclid.twjm/1500405962