Applications of Symmetric Quantum Calculus to Multivalent Functions in Geometric Function Theory

Abstract

This paper investigates multivalent analytic functions through the lens of symmetric quantum calculus. Using a generalized symmetric operator, we present novel classes of multivalent starlike functions in the framework of symmetric q-calculus linked with Janowski-type functions. We establish inclusion relationships among these classes and derive an adequate condition on coefficients for class membership. Towards the end of the paper, we develop several results on differential subordination, superordination, and sandwich-type theorems involving the same operator framework. These results include sharp bounds and identification of extremal dominant and subordinant functions. The work highlights the versatility of symmetric q-analytical approaches in geometric function analysis and provides a unified approach that extends several known existing contributions in the field.