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A Variational Technique for Bounded Starlike Functions

Published online by Cambridge University Press:  20 November 2018

R. W. Barnard
R. W. Barnard*
Affiliation:
Texas Tech University, Lubbock, Texas
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 2 , 01 April 1975 , pp. 337 - 347
Copyright
Copyright © Canadian Mathematical Society 1975

References

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