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

• Published in: AIMS mathematics Vol. 9; no. 12; pp. 33353 - 33364
• Main Authors: Louati, Hanen, Al-Rezami, Afrah, Deniz, Erhan, Darem, Abdulbasit, Szasz, Robert
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: (u, v) $-symmetrical functions $ (\rho, q) $-neighborhood; analytic functions; coefficient inequality; q $-calculus
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.20241591

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.