Uniqueness of first derivatives and differences in meromorphic functions and the characterization of entire function periodicity

Abhijit Banerjee; Sujoy Majumder; Nabadwip Sarkar

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arXiv · 2510.22277

Uniqueness of first derivatives and differences in meromorphic functions and the characterization of entire function periodicity

Abhijit Banerjee·Sujoy Majumder·Nabadwip Sarkar

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Abstract

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 $\Delta_cf(z)$. 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.]

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Abhijit Banerjee, Sujoy Majumder, Nabadwip Sarkar. 2025-10-25. Uniqueness of first derivatives and differences in meromorphic functions and the characterization of entire function periodicity. https://arxiv.org/abs/2510.22277

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