Moduli difference of inverse logarithmic coefficients of univalent functions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914465117634560 |
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| author | Allu, Vasudevarao Shaji, Amal |
| author_facet | Allu, Vasudevarao Shaji, Amal |
| contents | Let $f$ be analytic in the unit disk and $\mathcal{S}$ be the subclass of normalized univalent functions with $f(0) = 0$, and $f'(0) = 1$. Let $F$ be the inverse function of $f$, given by $F(w)=w+\sum_{n=2}^{\infty}A_nw^n$ defined on some disk $|w|\le r_0(f)$. The inverse logarithmic coefficients $Γ_n$, $n \in \mathbb{N}$, of $f$ are defined by the equation $ \log(F(w)/w)=2\sum_{n=1}^{\infty}Γ_{n}w^{n},\,|w|<1/4.$ In this paper, we find the sharp upper and lower bounds for moduli difference of second and first inverse logarithmic coefficients, {\em i.e.,} $|Γ_2|-|Γ_1|$ for functions in class $\mathcal{S}$ and for functions in some important subclasses of univalent functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10031 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moduli difference of inverse logarithmic coefficients of univalent functions Allu, Vasudevarao Shaji, Amal Complex Variables Let $f$ be analytic in the unit disk and $\mathcal{S}$ be the subclass of normalized univalent functions with $f(0) = 0$, and $f'(0) = 1$. Let $F$ be the inverse function of $f$, given by $F(w)=w+\sum_{n=2}^{\infty}A_nw^n$ defined on some disk $|w|\le r_0(f)$. The inverse logarithmic coefficients $Γ_n$, $n \in \mathbb{N}$, of $f$ are defined by the equation $ \log(F(w)/w)=2\sum_{n=1}^{\infty}Γ_{n}w^{n},\,|w|<1/4.$ In this paper, we find the sharp upper and lower bounds for moduli difference of second and first inverse logarithmic coefficients, {\em i.e.,} $|Γ_2|-|Γ_1|$ for functions in class $\mathcal{S}$ and for functions in some important subclasses of univalent functions. |
| title | Moduli difference of inverse logarithmic coefficients of univalent functions |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2403.10031 |