On certain non-linear differential monomial sharing non-zero polynomial
UDC 517.5 With the idea of normal family we study the uniqueness of meromorphic functions $f$ and $g$ when $f^{n}(\mathcal{L}(f))^{m}-p$ and $g^{n}(\mathcal{L}(g))^{m}-p$ share two values, where $\mathcal{L}(f)= a_{k}f^{(k)}+a_{k-1} f^{(k-1)}+\ldots+a_{1} f'+a_{0}f...
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| Datum: | 2021 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/99 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.5
With the idea of normal family we study the uniqueness of meromorphic functions $f$ and $g$ when $f^{n}(\mathcal{L}(f))^{m}-p$ and $g^{n}(\mathcal{L}(g))^{m}-p$ share two values, where $\mathcal{L}(f)= a_{k}f^{(k)}+a_{k-1} f^{(k-1)}+\ldots+a_{1} f'+a_{0}f,$ $a_{k}(\ne 0),a_{k-1},\ldots,a_{1},a_{0}\in\mathbb{C}$ and $p(z)(\not\equiv 0)$ is a polynomial. The obtained result significantly improves and generalizes the result in [A. Banerjee, S. Majumder, On certain non-linear differential polynomial sharing a non-zero polynomial, Bol. Soc. Mat. Mex. (2016),https://doi.org/10.1007/s40590-016-0156-0]. |
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| DOI: | 10.37863/umzh.v73i2.99 |