Entire function sharing two values partially with its derivative and a conjecture of Li and Yang

Abstract In the paper, using the idea of normal family, we investigate the uniqueness problem of entire functions that share two values partially with their k -th derivatives. The obtained results improve the results of Lü, Xu and Yi (Ann. Polon. Math. 95(1) (2009), 67–75) in a large scale. Also, as an application of our results, we have settled the conjecture posed by Li and Yang (Illinois J. Math. 44(2) (2000), 349–362).