Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 931981, 9 pages
doi:10.1155/2008/931981
Research Article
Coefficient Bounds for Certain Classes of Meromorphic Functions
1Department of Mathematics, College of Charleston, Charleston, SC 29424, USA
2Department of Applied Mathematics, Sri Venkateswara College of Engineering, Sriperumbudur, Chennai 602105, Tamilnadu, India
3School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
Received 19 May 2008; Revised 9 September 2008; Accepted 4 December 2008
Academic Editor: Ramm Mohapatra
Copyright © 2008 H. Silverman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Sharp bounds for |a1−μa02| are derived for certain classes Σ∗(ϕ) and
Σα∗(ϕ) of meromorphic functions f(z) defined on the punctured open unit disk for which −zf′(z)/f(z) and (−(1−2α)zf′(z)+αz2f″(z))/((1−α)f(z)−αzf′(z)) (α∈ℂ−(0,1]; ℜ(α)≥0), respectively, lie in a region starlike with respect to 1 and symmetric with
respect to the real axis. Also, certain applications of the main results for a
class of functions defined through Ruscheweyh derivatives are obtained.