Non-linear difference polynomials sharing a polynomial with finite weight
The uniqueness theory of meromorphic function mainly studies the conditions under which there exists only one function satisfying these conditions. The uniqueness theory of entire and meromorphic functions has grown up as an extensive sub-field of value distribution theory and the Nevanlinna's...
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| Format: | Article |
| Language: | English |
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Accademia Piceno Aprutina dei Velati
2024-01-01
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| Series: | Ratio Mathematica |
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| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/1421 |
| _version_ | 1797338090921000960 |
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| author | Harina Pandit Waghamore Preetham Nataraj Raj |
| author_facet | Harina Pandit Waghamore Preetham Nataraj Raj |
| author_sort | Harina Pandit Waghamore |
| collection | DOAJ |
| description | The uniqueness theory of meromorphic function mainly studies the conditions under which there exists only one function satisfying these conditions. The uniqueness theory of entire and meromorphic functions has grown up as an extensive sub-field of value distribution theory and the Nevanlinna's Five value and Four value theorems serves as the starting point of this uniqueness theory. In this paper, we consider a linear difference polynomial $\mathcal{L}_{\eta}(\mathfrak{f})=\mathfrak{f}(z+\eta)+\eta_0\mathfrak{f}(z)$, of the finite ordered non-constant meromorphic function $\mathfrak{f}$, with $\eta$ and $\eta_0$ being finite non-zero complex constants, and with the help of Nevanlinna theory, we analyse the uniqueness results between two finite ordered non-constant meromorphic functions $\mathfrak{f}$ and $\mathfrak{g}$, when their non-linear difference polynomials $\mathfrak{f}^n(z)\mathcal{L}_{\eta}(\mathfrak{f})$ and $\mathfrak{g}^n(z)\mathcal{L}_{\eta}(\mathfrak{g})$, with $n \ge 2$ being a positive integer shares a non-zero polynomial $p(z)$ with finite weights 0,1 and 2. Our results extend and improve some of the earlier results of Majumder (\textit{Applied Mathematics E-Notes, (17): 114-123, 2017) |
| first_indexed | 2024-03-08T09:26:02Z |
| format | Article |
| id | doaj.art-7af92b76c49a4ec3b1be71990bf8a183 |
| institution | Directory Open Access Journal |
| issn | 1592-7415 2282-8214 |
| language | English |
| last_indexed | 2024-03-08T09:26:02Z |
| publishDate | 2024-01-01 |
| publisher | Accademia Piceno Aprutina dei Velati |
| record_format | Article |
| series | Ratio Mathematica |
| spelling | doaj.art-7af92b76c49a4ec3b1be71990bf8a1832024-01-31T10:00:56ZengAccademia Piceno Aprutina dei VelatiRatio Mathematica1592-74152282-82142024-01-0151010.23755/rm.v51i0.1421898Non-linear difference polynomials sharing a polynomial with finite weightHarina Pandit Waghamore0Preetham Nataraj Raj1Bangalore UniversityBangalore UniversityThe uniqueness theory of meromorphic function mainly studies the conditions under which there exists only one function satisfying these conditions. The uniqueness theory of entire and meromorphic functions has grown up as an extensive sub-field of value distribution theory and the Nevanlinna's Five value and Four value theorems serves as the starting point of this uniqueness theory. In this paper, we consider a linear difference polynomial $\mathcal{L}_{\eta}(\mathfrak{f})=\mathfrak{f}(z+\eta)+\eta_0\mathfrak{f}(z)$, of the finite ordered non-constant meromorphic function $\mathfrak{f}$, with $\eta$ and $\eta_0$ being finite non-zero complex constants, and with the help of Nevanlinna theory, we analyse the uniqueness results between two finite ordered non-constant meromorphic functions $\mathfrak{f}$ and $\mathfrak{g}$, when their non-linear difference polynomials $\mathfrak{f}^n(z)\mathcal{L}_{\eta}(\mathfrak{f})$ and $\mathfrak{g}^n(z)\mathcal{L}_{\eta}(\mathfrak{g})$, with $n \ge 2$ being a positive integer shares a non-zero polynomial $p(z)$ with finite weights 0,1 and 2. Our results extend and improve some of the earlier results of Majumder (\textit{Applied Mathematics E-Notes, (17): 114-123, 2017)http://eiris.it/ojs/index.php/ratiomathematica/article/view/1421meromorphic functionsdifference polynomialsweighted sharinguniqueness |
| spellingShingle | Harina Pandit Waghamore Preetham Nataraj Raj Non-linear difference polynomials sharing a polynomial with finite weight Ratio Mathematica meromorphic functions difference polynomials weighted sharing uniqueness |
| title | Non-linear difference polynomials sharing a polynomial with finite weight |
| title_full | Non-linear difference polynomials sharing a polynomial with finite weight |
| title_fullStr | Non-linear difference polynomials sharing a polynomial with finite weight |
| title_full_unstemmed | Non-linear difference polynomials sharing a polynomial with finite weight |
| title_short | Non-linear difference polynomials sharing a polynomial with finite weight |
| title_sort | non linear difference polynomials sharing a polynomial with finite weight |
| topic | meromorphic functions difference polynomials weighted sharing uniqueness |
| url | http://eiris.it/ojs/index.php/ratiomathematica/article/view/1421 |
| work_keys_str_mv | AT harinapanditwaghamore nonlineardifferencepolynomialssharingapolynomialwithfiniteweight AT preethamnatarajraj nonlineardifferencepolynomialssharingapolynomialwithfiniteweight |