ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH FINITE GROWTH INDEX SHARING SOME SMALL FUNCTIONS
DOI:
https://doi.org/10.18173/2354-1059.2024-0003Keywords:
meromorphic function, unicity, complex discAbstract
In this paper, we will prove a uniqueness theorem for meromorphic functions with finite growth indices on a complex disc sharing some small functions with different multiplicity values. Intersecting points between these mappings and small functions with multiplicities more than a certain number do not need to be counted. Our result extends some previous results on this topic.
References
[1] Nevanlinna R, (1926). Einige Eideutigkeitssate in der theorie der meromorphen ¨funktionen. Acta Mathematica, 48, 367-391.
[2] Si DQ, (2012). Unicity of meromorphic functions sharing some small function. International Journal of Mathematics, 23(9), 1250088.
[3] Yamanoi K, (2004). The second main theorem for small functions and related problems. Acta Mathematica, 192, 225–294.
[4] Yi HX, (2002). On one problem of uniqueness of meromorphic functions concerning small functions. Proceedings of the American Mathematical Society, 130, 1689–1697.
[5] Yi HX & Yang CC, (1995) Uniqueness Theory of Meromorphic Functions. Pure and Applied Mathematics Monographs, 32.
[6] Yuhua L & Jianyong Q, (1999). On the uniqueness of meromorphic functions concerning small functions. Science in China, Series A, 29, 891–900.
[7] Ru M & Sibony N, (2020). The second main theorem in the hyperbolic case. Mathematische Annalen, 377, 759–795.
[8] Si DQ, (2024). Second main theorem and uniqueness problem of meromorphic functions with fnite growth index sharing fve small function on a complex disc. Chinese Annals of Mathematics, Series B.
