International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 830592, 9 pages
Research Article

Generalized Alpha-Close-to-Convex Functions

1Department of Mathematics, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan
2Department of Mathematics, Faculty of Science, Ataturk University, 25240 Erzurum, Turkey

Received 5 January 2009; Revised 26 June 2009; Accepted 13 September 2009

Academic Editor: Teodor Bulboacă

Copyright © 2009 K. Inayat Noor 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.


We define the classes Gβ(α,k,γ) as follows: fGβ(α,k,γ) if and only if, for zE={z:|z|<1}, |arg{(1-α2z2)f(z)/eiβϕ(z)}|γπ/2, 0<γ1; α[0,1]; β(π/2,π/2), where ϕ is a function of bounded boundary rotation. Coefficient estimates, an inclusion result, arclength problem, and some other properties of these classes are studied.