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Generalization properties for certain analytic functions. (English) Zbl 0924.30007
The results obtained by H. Saitoh (Math. Jap. 35, No. 6, 1073-1076 (1990; Zbl 0723.30009)] on a set of functions of the type \[ F(\alpha,\beta,z) =\alpha f(z)+\beta zf'(z) \] where \(f(z) = z + a_{n+1}z^{n+1} +\dots\) are analytic in the open unit disk, are generalized.
The proofs of these generalizations have been made by means of the well-known method, called that “of admissible functions” based on differential subordinations, order 1 and 2, introduced by S. S. Miller and P. T. Mocanu in 1978 and developed later on.

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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