Geometric Properties for Subclasses of Multivalent Analytic Functions Associated with q-Calculus Operator

This paper presents new subclasses of multivalent analytic functions defined through the q-derivative operator and examines their inclusion properties. By employing the Jackson q-derivative, we construct generalized operators that encompass numerous previously established operators and provide a framework for defining new classes with distinctive analytic features. Our main results are derived using techniques from differential subordination theory for complex-valued functions of one variable. Some applications of Bernardi operator are discussed.