Extremal problems in the class σ(Τ)

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Let Lf(r)={w=f(x), |z|=r}, 1 < r < ∞, be a level line of the function f(z) ∃ σ. Sharp upper bounds are obtained for the diameter of the curve Lf(r) in the class σ(Τ) for functions f(z)=z+α01z-1+... ∃ σ for which there exists a domain δf that complements the exterior of the unit disk and has conformal radius at the point w=0 satisfying the condition R(δf,0) ≥ Τ, 0 < Τ < 1. Also, a set of values is found for the coefficient α1 in the class σ(Τ).

Original languageEnglish
Pages (from-to)2152-2161
Number of pages10
JournalJournal of Mathematical Sciences
Issue number6
StatePublished - Aug 1994


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