Subordinations and superordinations studies using $ q $-difference operator

Abstract

The results of this work belong to the field of geometric function theory, being based on differential subordination methods. Using the idea of the $ \mathfrak{q} $-calculus operators, we define the $ \mathfrak{q} $-analogue of the multiplier- Ruscheweyh operator of a specific family of linear operators, $ I_{\mathfrak{q}, \mu }^{s}(\lambda, \ell). $ Our major goal is to build and investigate some analytic function subclasses using $ I_{\mathfrak{q}, \mu }^{s}(\lambda, \ell) $. Also, some differential subordination and superordination results are obtained. Moreover, based on the new theoretical results, several examples are constructed. For every differential superordination under investigation, the best subordinant is provided.

Keywords

• analytic function
• differential subordination
• superordination
• $ \mathfrak{q} $-difference operator
• $ \mathfrak{q} $-analogue catas operator
• $ \mathfrak{q} $-analogue of ruscheweyh operator