Geometric properties of a new subclass of harmonic functions defined by q-differential inequality

This paper introduces a novel subclass of q-harmonic functions in the open unit disk, defined via an inequality involving the q-derivative operator. The geometric properties of this class, particularly its close-to-convexity characteristics, are investigated. Main results include coefficient bounds, growth estimates, and a sufficient coefficient condition ensuring class membership. Additionally, the closure properties of this subclass under convolution and convex combination are examined, highlighting its structural stability. By incorporating q-calculus, this study extends existing results in harmonic function theory and provides new insights into the geometric behavior of these functions.