The sharp refined Bohr inequalities for a subclass of close-to-convex harmonic mappings
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| Format: | Preprint |
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2026
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| _version_ | 1866910221608157184 |
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| author | Kumar, Ayush |
| author_facet | Kumar, Ayush |
| contents | Let $\mathcal{H}$ be the class of normalized complex valued harmonic functions $ f = h + \overline{g}$ defined on the unit disk $\mathbb{D}$, where $h$ and $g$ are analytic functions with the normalization conditions $h(0) = h'(0) - 1 = 0$ and $g(0) = 0$. For the class $R_H^{0}(γ, δ, λ)$ ( $0 \leq λ< γ\leq δ$) consisting of functions \( f = h+\bar{g} \in \mathcal{H}\) satisfying the condition $f_{\overline{z}}(0)=0$ and the inequality $ Re(γh'(z)+δz h''(z) +(\frac{δ- γ}{2})z^2 h'''(z)-λ)> |γg'(z)+δz g''(z) +(\frac{δ- γ}{2})z^2 g'''(z)|$, we obtain sharp improved Bohr Phenomenon, refined Bohr radius and the Bohr-Rogosinski inequality for the class $R_H^{0}(γ, δ, λ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14776 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The sharp refined Bohr inequalities for a subclass of close-to-convex harmonic mappings Kumar, Ayush Complex Variables 30C45, 30C50, 30C80 Let $\mathcal{H}$ be the class of normalized complex valued harmonic functions $ f = h + \overline{g}$ defined on the unit disk $\mathbb{D}$, where $h$ and $g$ are analytic functions with the normalization conditions $h(0) = h'(0) - 1 = 0$ and $g(0) = 0$. For the class $R_H^{0}(γ, δ, λ)$ ( $0 \leq λ< γ\leq δ$) consisting of functions \( f = h+\bar{g} \in \mathcal{H}\) satisfying the condition $f_{\overline{z}}(0)=0$ and the inequality $ Re(γh'(z)+δz h''(z) +(\frac{δ- γ}{2})z^2 h'''(z)-λ)> |γg'(z)+δz g''(z) +(\frac{δ- γ}{2})z^2 g'''(z)|$, we obtain sharp improved Bohr Phenomenon, refined Bohr radius and the Bohr-Rogosinski inequality for the class $R_H^{0}(γ, δ, λ)$. |
| title | The sharp refined Bohr inequalities for a subclass of close-to-convex harmonic mappings |
| topic | Complex Variables 30C45, 30C50, 30C80 |
| url | https://arxiv.org/abs/2605.14776 |