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

Abstract

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.

Keywords

• analytic functions
• $ q $-calculus
• $ (u， v) $-symmetrical functions $ (\rho， q) $-neighborhood
• coefficient inequality