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Generalized hypergeometric functions associated with \(k\)-uniformly convex functions. (English) Zbl 1036.33003
Summary: For a certain linear operator which is defined by means of the Hadamard product (or convolution) with a generalized hypergeometric function, the authors aim at investigating various mapping and inclusion properties involving such subclasses of analytic and univalent functions as (for example) \(k\)-uniformly convex functions and \(k\)-starlike functions. Relevant connections of the definitions and results presented in this paper with those in several earlier works on the subject are also pointed out.

MSC:
33C20 Generalized hypergeometric series, \({}_pF_q\)
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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