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A Variational Technique for Bounded Starlike Functions
Published online by Cambridge University Press: 20 November 2018
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Let KM = {z : \z\ < M}, 1 ≦ M < ∞ and K = K1. Let S denote the collection of functions f(z) = z + a2z2 + a3s3 + … that are regular and univalent in K. We write, for 1 < M < ∞,
S(M) = ﹛f : f ∞ S, f (K) ⊂ KM ﹜,
S*(M) = ﹛f : f ∞ S(M), f(K) is starlike with respect to the origin﹜.
In this paper we develop a variational technique for slit domains and give some applications with respect to finding the
and the
for any nonconstant entire function ᶲ(w) and a given z ∊ K.
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- Copyright © Canadian Mathematical Society 1975
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