Uniqueness of first derivatives and differences in meromorphic functions and the characterization of entire function periodicity
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911231339659264 |
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| author | Banerjee, Abhijit Majumder, Sujoy Sarkar, Nabadwip |
| author_facet | Banerjee, Abhijit Majumder, Sujoy Sarkar, Nabadwip |
| contents | The objective of the paper is twofold. The first objective is to study the uniqueness problem of meromorphic function $f(z)$ when $f^{(1)}(z)$ shares two distinct finite values $a_1$, $a_2$ and $\infty$ CM with $Δ_cf(z)$. In this context, we provide a result that resolves the open problem posed by Qi et al. [Comput. Methods Funct. Theory, 18 (2018), 567-582] for the case when hyper order of the function is less than $\infty$. The second objective is to establish sufficient conditions for the periodicity of transcendental entire functions. In this direction, we obtain a result that affirms the question raised by Wei et al. [Anal. Math., 47 (2021), 695-708.] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness of first derivatives and differences in meromorphic functions and the characterization of entire function periodicity Banerjee, Abhijit Majumder, Sujoy Sarkar, Nabadwip Complex Variables 39A05, 30D35, 39A45 The objective of the paper is twofold. The first objective is to study the uniqueness problem of meromorphic function $f(z)$ when $f^{(1)}(z)$ shares two distinct finite values $a_1$, $a_2$ and $\infty$ CM with $Δ_cf(z)$. In this context, we provide a result that resolves the open problem posed by Qi et al. [Comput. Methods Funct. Theory, 18 (2018), 567-582] for the case when hyper order of the function is less than $\infty$. The second objective is to establish sufficient conditions for the periodicity of transcendental entire functions. In this direction, we obtain a result that affirms the question raised by Wei et al. [Anal. Math., 47 (2021), 695-708.] |
| title | Uniqueness of first derivatives and differences in meromorphic functions and the characterization of entire function periodicity |
| topic | Complex Variables 39A05, 30D35, 39A45 |
| url | https://arxiv.org/abs/2510.22277 |