International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 830592, 9 pages
doi:10.1155/2009/830592

Generalized alpha-close-to-convex functions

K.Inayat Noor1 , Halit Orhan2 and Saima Mustafa1

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

Abstract

We define the classes Gβ(α,k,γ) as follows: f∈Gβ(α,k,γ) if and only if, for z∈E={z∈ℂ:|z|<1}, |arg{(1-α2z2)f′(z)/e−iβϕ′(z)}|≤γπ/2, 0<γ≤1; 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.