Application of $q$-starlike and $q$-convex functions under $(u,v)$-symmetrical constraints

This research paper addressed a significant knowledge gap in the field of complex analysis by introducing a pioneering category of $q$-starlike and $q$-convex functions intricately interconnected with $(u,v)$-symmetrical functions. Recognizing the limited exploration of these relationships in existing literature, the authors delved into the new classes ${\mathcal{S}}_q(\alpha ,u,v)$ and ${\mathcal{T}}_q(\alpha ,u,v)$. The main contribution of this work was the establishment of a framework that amalgamates $q$-starlikeness and $q$-convexity with the symmetry conditions imposed by $(u,v)$-symmetrical functions. This comprehensive study include coefficient estimates, convolution conditions, and the properties underpinning the $(\rho ,q)$-neighborhood, thereby enriching the understanding of these novel function classes.