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Journal of the London Mathematical Society 1981 s2-24(3):495-501; doi:10.1112/jlms/s2-24.3.495
© 1981 by London Mathematical Society
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© Oxford University Press

On the Normality of Derivatives of Functions, II

Peter Lappan

Department of Mathematics, Michigan State University, East Lansing Michigan 48824, U.S.A.

In answer to the author's question in the original paper of the same title, it is proved that given a set E of positive integers there exists a bounded analytic function G(z) in the unit disc such that the k-th derivative G(k)(z) is a normal function if and only if k {notin} E. Also, an example of a univalent function is given for which the integral is not a normal function. This example leads to an explicit example of a non-normal locally uniformly univalent function.


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