Vol. 38, No. 3, 1971

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On the multivalence of a class of meromorphic functions

Zalman Rubinstein

Vol. 38 (1971), No. 3, 771–784

The estimates are given for the radius of the largest disk about the origin on which all the functions of the form a∕z + ϕ(z) are p-valent, where ϕ(z) is an analytic function defined in the unit disk and of modulus less than unity there. Similar results are obtained concerning the starlikeness of the image of circles about the origin.

Suppose a polynomial of degree n assumes p-times a certain value in the center of a circle and does not take this value elsewhere in this circle. The author determines the largest concentric circle in which the polynomial is p-valent. The same problem is then considered in a more general setting and similar results are obtained.

Mathematical Subject Classification
Primary: 30A36
Received: 13 August 1970
Revised: 19 April 1971
Published: 1 September 1971
Zalman Rubinstein