Application of $ q $-starlike and $ q $-convex functions under $ (u, v) $-symmetrical constraints - Louati, Hanen; Al-Rezami, Afrah; Deniz, Erhan; Darem, Abdulbasit; Szasz, Robert (AIMS mathematics, 2024)
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(α, u, v) $ and $ \mathcal{T}_q(α, 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 $ (ρ, q) $-neighborhood, thereby enriching the understanding of these novel function classes.