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...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241591 |
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| Summary: | 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. |
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| ISSN: | 2473-6988 |