New Subclass of Convex Functions Concerning Infinite Cone
We introduce a new subclass of convex functions as follows:\[ \mathcal{K}_{IC}:=\left\{f\in \mathcal{A}:{\rm Re}\left(1+\frac{zf''(z)}{f'(z)}\right)>\left|f'(z)-1\right|,\quad |z|<1\right\},\]where $\mathcal{A}$ denotes the class of analytic and normalized functions in t...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2024-03-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_709283_84739b66a34d93ea1b4d5887d2ebc69b.pdf |
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| Summary: | We introduce a new subclass of convex functions as follows:\[ \mathcal{K}_{IC}:=\left\{f\in \mathcal{A}:{\rm Re}\left(1+\frac{zf''(z)}{f'(z)}\right)>\left|f'(z)-1\right|,\quad |z|<1\right\},\]where $\mathcal{A}$ denotes the class of analytic and normalized functions in the unit disk $|z|<1$. Some properties of this particular class, including subordination relation, integral representation, the radius of convexity, rotation theorem, sharp coefficients estimate and Fekete-Szeg\"{o} inequality associated with the $k$-th root transform, are investigated. |
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| ISSN: | 2322-5807 2423-3900 |