Abstract and Applied Analysis
Volume 2011 (2011), Article ID 849250, 9 pages
http://dx.doi.org/10.1155/2011/849250
Research Article

Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function

G. Murugusundaramoorthy,1 K. Uma,1 and M. Darus2

1School of Advanced Sciences, VIT University, Vellore 632014, India
2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia

Received 29 January 2011; Accepted 7 April 2011

Academic Editor: Yoshikazu Giga

Copyright © 2011 G. Murugusundaramoorthy 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

Let 𝑓 𝑛 ∑ ( 𝑧 ) = 𝑧 + 𝑛 𝑘 = 2 𝑎 𝑘 𝑧 𝑘 be the sequence of partial sums of the analytic function ∑ 𝑓 ( 𝑧 ) = 𝑧 + ∞ 𝑘 = 2 𝑎 𝑘 𝑧 𝑘 . In this paper, we determine sharp lower bounds for ℜ { 𝑓 ( 𝑧 ) / 𝑓 𝑛 ( 𝑧 ) } , ℜ { 𝑓 𝑛 ( 𝑧 ) / 𝑓 ( 𝑧 ) } , ℜ { 𝑓 ( 𝑧 ) / 𝑓 𝑛 ( 𝑧 ) } , and ℜ { 𝑓 𝑛 ( 𝑧 ) / 𝑓 ( 𝑧 ) } . The usefulness of the main result not only provides the unification of the results discussed in the literature but also generates certain new results.