Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial
Let $k$ be a nonnegative integer or infinity. For $a\in\mathbb{C}\cup\{\infty\}$ we denote by $E_k(a;f)$ the set of all $a$-points of $f$ where an $a$-point of multiplicity $m$ is counted $m$ times if $m\leq k$ and $k+1$ times if $m>k$. If $E_k(a;f)= E_k(a;g)$ then we say that $f$ and $g$ sha...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2016-10-01
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| Series: | Mathematica Bohemica |
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| Online Access: | http://mb.math.cas.cz/full/141/3/mb141_3_1.pdf |
| _version_ | 1819156707802087424 |
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| author | Pulak Sahoo |
| author_facet | Pulak Sahoo |
| author_sort | Pulak Sahoo |
| collection | DOAJ |
| description | Let $k$ be a nonnegative integer or infinity. For $a\in\mathbb{C}\cup\{\infty\}$ we denote by $E_k(a;f)$ the set of all $a$-points of $f$ where an $a$-point of multiplicity $m$ is counted $m$ times if $m\leq k$ and $k+1$ times if $m>k$. If $E_k(a;f)= E_k(a;g)$ then we say that $f$ and $g$ share the value $a$ with weight $k$. Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to Xia and Xu (2011) and the results of Li and Yi (2011). |
| first_indexed | 2024-12-22T15:57:09Z |
| format | Article |
| id | doaj.art-cfbf61347cc84fc795c70c526cf2358a |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-12-22T15:57:09Z |
| publishDate | 2016-10-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-cfbf61347cc84fc795c70c526cf2358a2022-12-21T18:20:46ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362016-10-01141329731310.21136/MB.2016.0018-14MB.2016.0018-14Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomialPulak SahooLet $k$ be a nonnegative integer or infinity. For $a\in\mathbb{C}\cup\{\infty\}$ we denote by $E_k(a;f)$ the set of all $a$-points of $f$ where an $a$-point of multiplicity $m$ is counted $m$ times if $m\leq k$ and $k+1$ times if $m>k$. If $E_k(a;f)= E_k(a;g)$ then we say that $f$ and $g$ share the value $a$ with weight $k$. Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to Xia and Xu (2011) and the results of Li and Yi (2011).http://mb.math.cas.cz/full/141/3/mb141_3_1.pdf uniqueness meromorphic function differential polynomial weighted sharing |
| spellingShingle | Pulak Sahoo Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial Mathematica Bohemica uniqueness meromorphic function differential polynomial weighted sharing |
| title | Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial |
| title_full | Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial |
| title_fullStr | Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial |
| title_full_unstemmed | Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial |
| title_short | Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial |
| title_sort | uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial |
| topic | uniqueness meromorphic function differential polynomial weighted sharing |
| url | http://mb.math.cas.cz/full/141/3/mb141_3_1.pdf |
| work_keys_str_mv | AT pulaksahoo uniquenessanddifferentialpolynomialsofmeromorphicfunctionssharinganonzeropolynomial |