Abstract: | In the class F1 of functions f(), regular and univalent in the annulus ={<||<1} and satisfying the conditions ¦f()¦ < 1 and f() 0 for , ¦f()¦=1 ¦¦=1, for f(l)=1, one finds the set of the values D(A)=f(A): f for an arbitrary fixed point A. One makes use of the method of variations and certain facts from the theory of the moduli of families of curves.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 82–92, 1985. |