Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4633416 | Applied Mathematics and Computation | 2009 | 15 Pages |
Abstract
For a complex number αα with Reα>0 let Kϕ(α)Kϕ(α) be the class of analytic functions f in the unit disk DD with f(0)=0f(0)=0 satisfying Re(f′(z)/ϕ′(z))>0 in D,f′(0)/ϕ′(0)=α, for some convex univalent function ϕϕ in DD. For any fixed z0∈Dz0∈D, and λ∈D¯ we shall determine the region of variability Vϕ(z0,α,λ)Vϕ(z0,α,λ) for f(z0)f(z0) when f ranges over the classKϕ(α,λ)=f∈Kϕ(α):ddzf′(z)ϕ′(z)z=0=2λ(Reα).In the final section we graphically illustrate the region of variability for several sets of parameters z0z0 and αα.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
S. Ponnusamy, A. Vasudevarao, H. Yanagihara,