Abstract
Suppose that f(z) is a nonconstant meromorphic function of hyper order strictly less than 1, c is a nonzero finite constant, a, b are distinct finite constants, and \(n\ge 1\), \(k\ge 0\) are all integers. In this paper, we firstly prove one uniqueness theorem when f(z) and \((\Delta ^{n}_{c}f(z))^{(k)}\) share \(a,\infty\) CM and share b IM with additional conditions and give some further discussions. We also prove another uniqueness theorem when \(f'(z)\) and \(f(z+c)\) share \(\infty\) CM and share a, b IM. Our main theorems generalize and improve many recent known results.
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Wang, MH., Chen, JF. Uniqueness of meromorphic functions concerning their differential-difference operators. J Anal (2024). https://doi.org/10.1007/s41478-024-00773-w
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DOI: https://doi.org/10.1007/s41478-024-00773-w