International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 356915, 8 pages
http://dx.doi.org/10.1155/2011/356915
Research Article

The Generalized Janowski Starlike and Close-to-Starlike Log-Harmonic Mappings

Maisarah Haji Mohd and Maslina Darus

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor D. Ehsan, Malaysia

Received 16 April 2011; Accepted 17 August 2011

Academic Editor: A. Zayed

Copyright © 2011 Maisarah Haji Mohd and Maslina 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

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form 𝑓 ( 𝑧 ) = 𝑧 ℎ ( 𝑧 ) 𝑔 ( 𝑧 ) defined on the open unit disc 𝑈 . The functions are in the class of the generalized Janowski starlike log-harmonic mapping, 𝑆 ∗ l h ( 𝐴 , 𝐵 , 𝛼 ) , with the functional 𝑧 ℎ ( 𝑧 ) in the class of the generalized Janowski starlike functions, 𝑆 ∗ ( 𝐴 , 𝐵 , 𝛼 ) . By means of these functions, we obtained results on the generalized Janowski close-to-starlike log-harmonic mappings, 𝐶 𝑆 𝑇 l h ( 𝐴 , 𝐵 , 𝛼 ) .