On Properties of q-Close-to-Convex Harmonic Functions of Order α

In this paper, a novel subclass, denoted as PH(q, α), is unveiled within the domain of harmonic functions in the open unit disk E. This subclass, comprised of functions f = u + v ∈ SH0 , is characterized by a specific inequality involving the q-derivative operator. Through meticulous analysis, it is demonstrated that functions belonging to PH(q, α) exhibit remarkable close-to-convexity properties. Furthermore, diverse results such as distortion theorem, coefficient bounds, and a sufficient coefficient condition are yielded by the exploration. Additionally, the closure properties of PH(q, α) under convolution operations and convex combination are elucidated, underscoring its structural coherence and relevance in the broader context of harmonic mappings.