Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions
UDC 517.5 We establish several sharp versions of Bohr's inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings on the unit disk $\mathbb{D} := \{z \in \mathbb{C}\colon |z| < 1\}$ by using a sequence $\{\Psi_n(r)\}_{n=0}^\infty$ of nonnegative continuo...
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| Datum: | 2026 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9269 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513454722383873 |
|---|---|
| author | Biswas, Raju Mandal, Rajib Biswas, Raju Mandal, Rajib |
| author_facet | Biswas, Raju Mandal, Rajib Biswas, Raju Mandal, Rajib |
| author_sort | Biswas, Raju |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:36:04Z |
| description | UDC 517.5
We establish several sharp versions of Bohr's inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings on the unit disk $\mathbb{D} := \{z \in \mathbb{C}\colon |z| < 1\}$ by using a sequence $\{\Psi_n(r)\}_{n=0}^\infty$ of nonnegative continuous functions defined on $[0,1)$ and such that the series $\sum_{n=0}^\infty \Psi_n(r)$ converges locally uniformly in $[0,1).$ As an application, we deduce several well-known results, as well as numerous improved and refined Bohr's inequalities for harmonic mappings in the unit disk $\mathbb{D}.$ |
| doi_str_mv | 10.3842/umzh.v77i12.9269 |
| first_indexed | 2026-03-24T03:44:57Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9269 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:44:57Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-92692026-03-21T13:36:04Z Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions Biswas, Raju Mandal, Rajib Biswas, Raju Mandal, Rajib Harmonic mappings locally univalent functions Bohr inequality K-quasiconformal mappings 30B10 30C62 30C75 40A30 30A10 UDC 517.5 We establish several sharp versions of Bohr's inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings on the unit disk $\mathbb{D} := \{z \in \mathbb{C}\colon |z| < 1\}$ by using a sequence $\{\Psi_n(r)\}_{n=0}^\infty$ of nonnegative continuous functions defined on $[0,1)$ and such that the series $\sum_{n=0}^\infty \Psi_n(r)$ converges locally uniformly in $[0,1).$ As an application, we deduce several well-known results, as well as numerous improved and refined Bohr's inequalities for harmonic mappings in the unit disk $\mathbb{D}.$ УДК 517.5 Нерівності Бора, пов'язані з множиною всіх послідовностей невід'ємних неперервних функцій Встановлено кілька точних варіантів нерівностей Бора для класу $K$-квазіконформних гармонічних відображень, що зберігають сенс в одиничному крузі $\mathbb{D} := \{z \in \mathbb{C}\colon |z| < 1\},$ із використанням послідовності $\{\Psi_n(r)\}_{n=0}^\infty$ невід'ємних неперервних функцій, визначених на відрізку $[0,1)$, для якої ряд $\sum_{n=0}^\infty \Psi_n(r)$ збігається локально рівномірно в $[0,1).$ Як застосування, наведено кілька відомих результатів, а також отримано низку покращених й уточнених нерівностей Бора для гармонічних відображень в одиничному крузі $\mathbb{D}.$ Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9269 10.3842/umzh.v77i12.9269 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 12 (2025); 743–744 Український математичний журнал; Том 77 № 12 (2025); 743–744 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9269/10609 Copyright (c) 2025 Raju Biswas, Rajib Mandal |
| spellingShingle | Biswas, Raju Mandal, Rajib Biswas, Raju Mandal, Rajib Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions |
| title | Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions |
| title_alt | Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions |
| title_full | Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions |
| title_fullStr | Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions |
| title_full_unstemmed | Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions |
| title_short | Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions |
| title_sort | bohr's inequalities associated with the set of all sequences of nonnegative continuous functions |
| topic_facet | Harmonic mappings locally univalent functions Bohr inequality K-quasiconformal mappings 30B10 30C62 30C75 40A30 30A10 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9269 |
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