International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 520698, 11 pages
doi:10.1155/2008/520698
Research Article
On Integral Operator Defined by Convolution Involving Hybergeometric Functions
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Darul Ehsan, Malaysia
Received 16 September 2007; Accepted 9 January 2008
Academic Editor: Brigitte Forster-Heinlein
Copyright © 2008 K. Al-Shaqsi and M. Darus. 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
For λ>−1 and μ≥0, we consider a liner operator Iλμ on the class 𝒜 of analytic functions in the unit disk defined by the convolution (fμ)(−1)∗f(z), where fμ=(1−μ)z2F1(a,b,c;z)+μz(z2F1(a,b,c;z))', and introduce a certain new subclass of 𝒜 using this operator. Several interesting properties of these classes are obtained.