Differential Subordination and Differential Superordination for Classes of Admissible Multivalent Functions Associated with a Linear Operator

Abstract

In this paper, we first introduce a linear integral operator ℑp(a,c,μ)(μ>0;a,c∈R;c>a>−μp;p∈N+:={1,2,3,…}), which is somewhat related to a rather specialized form of the Riemann–Liouville fractional integral operator and its varied form known as the Erdélyi–Kober fractional integral operator. We then derive some differential subordination and differential superordination results for analytic and multivalent functions in the open unit disk U, which are associated with the above-mentioned linear integral operator ℑp(a,c,μ). The results presented here are obtained by investigating appropriate classes of admissible functions. We also obtain some Sandwich-type results.

Keywords

• analytic functions
• univalent
• multivalent functions
• differential subordination
• differential superordination
• sandwich-type theorems