Hypergeometric functions in the parabolic starlike and uniformly convex domains

Abstract

For a sufficiently adequate special case of the Dziok–Srivastava linear operator defined by means of the Hadamard product (or convolution) with a generalized hypergeometric function, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, which are introduced here. Relevant connections of the definitions and results presented in this paper with those in several earlier works on the subject are also pointed out.

Keywords:

• Generalized hypergeometric function
• Dziok–Srivastava linear operator
• Parabolic starlike functions
• Uniformly starlike functions
• Uniformly convex functions
• Hadamard product (or convolution)

Acknowledgements

The present investigation was supported, in part, by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0007353.