Beta-Bazilevič Function
In this paper, we introduce a relatively new class, $\mathcal{\mathcal{B}}_{1}^\beta(\alpha)$, namely the class of Beta-Bazilevi\v{c} function is generated by the function Bazilevi\v{c} $\mathcal{B}_{1}(\alpha)$. We introduce the class in question by constructing the Alpha-Convex function, $\mathcal...
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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_709284_a224e0483a1dfcc3a1b3cd17429f06c1.pdf |
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| Summary: | In this paper, we introduce a relatively new class, $\mathcal{\mathcal{B}}_{1}^\beta(\alpha)$, namely the class of Beta-Bazilevi\v{c} function is generated by the function Bazilevi\v{c} $\mathcal{B}_{1}(\alpha)$. We introduce the class in question by constructing the Alpha-Convex function, $\mathcal{M}(\alpha)$, introduced by Miller et al. \cite{15}. Using Lemmas of function with positive real part, we were given a sharp estimate of coefficient problems. The coefficient problems to be solved are the modulus of initial coefficients $f$, the modulus of inverse coefficients $f^{-1}$, the modulus of the Logarithmic coefficients $\log \frac{f(z)}{z}$, the Fekete-Szeg\"{o} problem and the second Hankel determinant problem. |
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| ISSN: | 2322-5807 2423-3900 |