On the Largest Disc Mapped by Sum of Convex and Starlike Functions - Rosihan M. Ali; Naveen Kumar Jain; V. Ravichandran (Abstract and Applied Analysis)
For a normalized analytic function f defined on the unit disc 𝔻, let ϕ(f,f′,f′′;z) be a function of positive real part in 𝔻, ψ(f,f′,f′′;z) need not have that property in 𝔻, and χ=ϕ+ψ. For certain choices of ϕ and ψ, a sharp radius constant ρ is determined, 0<ρ<1, so that χ(ρz)/ρ maps 𝔻 onto a specified region in the right half-plane.