Subordinations and superordinations studies using $ q $-difference operator

Abstract

<abstract><p>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.</p></abstract>