New Subclass of Close-to-convex Functions Associated with the Vertical Strip Domains

In the present paper, we introduce the class Βθ(α,β) consisting of functions f, analytic in the unit disc ∆, normalized by the condition f(0)=0=f´(0)-1 and satisfying the following two-sided inequality α Re{f´(z)+(1+eiθ)/2 zf´´(z)} β (z∈∆), where θ∊(-π,π], 0≤α 1 and β 1. Integral representation, differential subordination results, coefficient estimates and Fekete-Szegö coefficient functional associated with the k-th (k≥1) root transform [f(zk)]1/k for functions in the class Βθ(α,β), are determined.