Year: 2025
Type: article
Abstract: Let f f be a transcendental entire function of hyperorder strictly less than 1, and let c c be a nonzero finite complex number. We prove that if f ( z ) f\left(z) and f ( z + c ) f\left(z+c) partially share 0, 1 ignoring multiplicity (i.e., E ¯ ( 0 , f ( z ) ) ⊆ E ¯ ( 0 , f ( z + c ) ) \overline{E}\left(0,f\left(z))\subseteq \overline{E}\left(0,f\left(z+c)) and E ¯ ( 1 , f ( z ) ) ⊆ E ¯ ( 1 , f ( z + c ) ) \overline{E}\left(1,f\left(z))\subseteq \overline{E}\left(1,f\left(z+c)) ), then f ( z ) ≡ f ( z + c ) f\left(z)\equiv f\left(z+c) . This result is a generalization and improvement of the previous theorem due to Li and Yi.
Source: Open Mathematics
Authors: Aizhu Xu, Peiqiang Lin, Shengjiang Chen
Institution: Ningde Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W4409504935