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.

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.