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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.

##### MSC:
 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
##### Keywords:
complex valued function
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