Taiwanese Journal of Mathematics

CLASSES OF MEROMORPHIC α-CONVEX FUNCTIONS

Rosihan M. Ali and V. Ravichandran

Full-text: Open access

Abstract

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 $\phi$.

Article information

Source
Taiwanese J. Math., Volume 14, Number 4 (2010), 1479-1490.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405962

Digital Object Identifier
doi:10.11650/twjm/1500405962

Mathematical Reviews number (MathSciNet)
MR2663926

Subjects
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

Keywords
convolution univalent meromorphic functions differential subordination and superordination

Citation

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


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