Differential subordination and superordination studies involving symmetric functions using a $q$-analogue multiplier operator

The present investigation focus on applying the theories of differential subordination, differential superordination and related sandwich-type results for the study of some subclasses of symmetric functions connected through a linear extended multiplier operator, which was previously defined by involving the $q$-Choi-Saigo-Srivastava operator. The aim of the paper is to define a new class of analytic functions using the aforementioned linear extended multiplier operator and to obtain sharp differential subordinations and superordinations using functions from the new class. Certain subclasses are highlighted by specializing the parameters involved in the class definition, and corollaries are obtained as implementations of those new results using particular values for the parameters of the new subclasses. In order to show how the results apply to the functions from the recently introduced subclasses, numerical examples are also provided.