On a Unified Subclass of Analytic Functions with Negative Coefficients Defined via a Generalized q-Calculus Operator

We introduce and analyze a subclass of analytic functions with negative coefficients, denoted by Pq,σm,ℓ,p(α,η), constructed through a generalized q-calculus operator in combination with a multiplier-type transformation. For this class, we obtain sharp coefficient bounds, growth and distortion estimates, and closure results. The radii of close-to-convexity, starlikeness, and convexity are determined, and further consequences, such as integral means inequalities and neighborhood characterizations, are derived. The results presented provide a broad framework that incorporates and extends several earlier families of analytic and geometric function classes.