Notes on entire functions sharing an entire function of a smaller order with their difference operators

摘要

In this paper, we study a uniqueness question of entire functions sharing an entire function of smaller order with their difference operators. The results in this paper extend Theorem 1. 1 in [19] by Liu and Yang and deal with Question 1 in [19], where the entire functions are of finite order. Moreover, we repair certain statements in [21] by Li et al., which in turn had depended on questionable assertions of Lemma 2. 6 in [20]. Examples are provided to show that the results in this paper are best possible.