Symmetric Properties of Janowski-Type q-Harmonic Close-to-Convex Functions

We introduce and study a new subclass of Janowski-type harmonic close-to-convex functions in the open unit disk defined via the Jackson q-derivative operator. The structure of the operator naturally reflects certain symmetric properties in the analytic representation of the considered harmonic mappings. By applying subordination techniques, we establish sufficient conditions for sense-preserving close-to-convexity and distortion estimates. The extreme points of the class are determined, and its topological properties are examined, showing that the class is convex and compact. We further obtain the radius of starlikeness and prove that the class is closed under convolution. Moreover, as q→1−, the operator reduces to the classical derivative, and our results recover several known results in the existing literature, demonstrating that the present work extends and generalizes earlier findings.