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On the Largest Disc Mapped by Sum of Convex and Starlike Functions
2013
Abstract and Applied Analysis
Preserved Fulltext
For a normalized analytic functionfdefined on the unit disc𝔻, letϕ(f,f′,f′′;z)be a function of positive real part in𝔻,ψ(f,f′,f′′;z)need not have that property in𝔻, andχ=ϕ+ψ. For certain choices ofϕandψ, a sharp radius constantρis determined,0<ρ<1, so thatχ(ρz)/ρmaps𝔻onto a specified region in the right half-plane.
doi:10.1155/2013/682413
fatcat:jstwuxxdz5dprpb4vqspwpwjbq