Uniqueness results for differential polynomials weighted sharing a set | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Volume 13, Issue 1, 2025, Pages 1-13 PDF (245.44 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2025.318717.1261 | ||
| Author | ||
| Jayanta Roy* | ||
| Centre for Distance and online Education, University of North Bengal, Raja Rammohunpur, Dist -Darjeeling, West Bengal, India, 734013 | ||
| Abstract | ||
| In this paper, we explore the uniqueness problem of differential polynomials $(Q(f))^{(k)}$ and $(Q(g))^{(k)}$ of meromorphic functions $f$ and $g$, respectively with the notion of weighted sharing a set of roots of unity, where $Q$ is a polynomial of one variable. The results of the paper generalize the results due to Sultana and Sahoo[ Mathematica Bohemica, 2024]. In this paper, the meromorphic function means the meromorphic function in the complex plane. We use the standard notations of Nevanlinna theory, which can be found in \cite{ hay, yang, yi}. A meromorphic function $a \ (\not\equiv 0,\infty)$ is said to be small with respect to $f$ provided $T(r,a)=S(r,f)$ as $r\rightarrow\infty, \ r\not\in E$ where $E$ is a set of positive real numbers of finite Lebesgue measure. We denote by $S(f)$ the collection of all small functions of $f$. For any two non-constant meromorphic functions $f$ and $g$, and $a\in S(f)\cap S(g)$, we say that $f$ and $g$ share $a$ CM(IM) provided that $f-a$ and $g-a$ have the same zeros counting (ignoring) multiplicities. | ||
| Keywords | ||
| Meromorphic function; Differential polynomial; Set sharing; Weighted sharing; Uniqueness | ||
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