Application of subordination and superordination for multivalent analytic functions associated with differintegral operator

Abstract

The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on the properties of the differential subordination and superordination one of the newest techniques used in this field, we obtain some differential subordination and superordination results for multivalent functions defined by differintegral operator with $ j $-derivatives $ \Im _{p}(\nu, \rho; \ell)f(z) $ for $ \ell > 0, \ \nu, \rho \in \mathbb{R}, \ $such that $ (\rho -j)\geq 0, \nu > -\ell p\, (p\in \mathbb{N}) $ in the open unit disk $ U $. Differential sandwich result is also obtained. Also, the results are followed by some special cases and counter examples.

Keywords

• analytic function
• multivalent functions
• higher order derivatives
• subordination
• superordination