Generalized Alpha-Close-to-Convex Functions

Abstract EN

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.