Some inclusion properties for certain subclasses of strongly starlike and strongly convex functions involving a family of fractional integral operators

Abstract

A known family of fractional integral operators (with the Gauss hypergeometric function in the kernel) is used here to define some new subclasses of strongly starlike and strongly convex functions of order β and type α in the open unit disk 𝕌. For each of these new function classes, several inclusion relationships associated with the fractional integral operators are established. Some interesting corollaries and consequences of the main inclusion relationships are also considered.

Keywords:

• Analytic functions
• Starlike functions
• Convex functions
• Close-to-convex functions
• Strongly starlike functions
• Strongly convex functions
• Gauss hypergeometric function
• Fractional integral operators
• Inclusion properties

Acknowledgements

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