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A certain class of functions that are univalent in an annulus

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Abstract

In the class F1 of functions f(ζ), regular and univalent in the annulus κ={ρ<|ζ|<1} and satisfying the conditions ¦f(ζ)¦ < 1 and f(ζ) ≠ 0 for ζ∃κ, ¦f(ζ)¦=1 ¦ζ¦=1, for f(l)=1, one finds the set of the values D(A)=f(A): f∃κ for an arbitrary fixed point A∃κ. One makes use of the method of variations and certain facts from the theory of the moduli of families of curves.

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Authors
  1. E. G. Emel'yanov
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 82–92, 1985.

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Emel'yanov, E.G. A certain class of functions that are univalent in an annulus. J Math Sci 38, 2090–2098 (1987). https://doi.org/10.1007/BF01474443

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