Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 346279, 9 pages
Research Article

Neighborhoods of Starlike and Convex Functions Associated with Parabola

Rosihan M. Ali,1 K. G. Subramanian,1 V. Ravichandran,2 and Om P. Ahuja3

1School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
2Department of Mathematics, University of Delhi, Delhi 110007, India
3Department of Mathematics, Kent State University, Burton, OH 44021-9500, USA

Received 16 June 2008; Accepted 11 August 2008

Academic Editor: Ramm Mohapatra

Copyright © 2008 Rosihan M. Ali 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.


Let f be a normalized analytic function defined on the unit disk and fλ(z):=(1λ)z+λf(z) for 0<λ1. For α>0, a function f𝒮𝒫(α,λ) if zf(z)/fλ(z) lies in the parabolic region Ω:={w:|wα|<Re ⁡w+α}. Let 𝒞𝒫(α,λ) be the corresponding class consisting of functions f such that (zf(z))/fλ(z) lies in the region Ω. For an appropriate δ>0, the δ-neighbourhood of a function f𝒞𝒫(α,λ) is shown to consist of functions in the class 𝒮𝒫(α,λ).