Subordination and superordination for multivalent functions associated with a class of fractional differintegral operators

Abstract

The purpose of the present paper is to investigate some subordination and superordination implications associated with a class of fractional differintegral operators, which are obtained by considering suitable classes of admissible multivalent analytic functions. The sandwich-type theorems for these operators are also considered.

Keywords:

• differential subordination
• differential superordination
• analytic functions
• univalent functions
• multivalent functions
• convex functions
• fractional differintegral operators
• sandwich-type theorems
• Dziok–Srivastava operator
• generalized hypergeometric function

2000 Mathematics Subject Classifications :

• Primary: 26A33
• 30C45
• Secondary: 33B15
• 33C20

Acknowledgements

This work was supported by the Korea Research Foundation Grant funded by the Government of the Republic of Korea (MOEHRD: Basic Research Promotion Fund) (KRF-2008-313-C00035) and, in part, by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0007353.