A class of nonlinear integral operators preserving subordination and superordination

Abstract

In the present article, we obtain the subordination- and superordination-preserving properties of certain nonlinear integral operators defined on the space of normalized analytic functions in the open unit disk. A differential sandwich-type theorem for these integral operators is also presented.

Keywords:

• Differential subordination and superordination
• Analytic functions
• Univalent functions
• Starlike functions
• Convex functions
• Integral operators

Acknowledgements

This work was supported, in part, by the Korea Research Foundation Grant funded by the Government of the Republic of Korea (MOEHRD)(KRF-2006-521-C00008) and, in part, by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0007353.