On one problem of uniqueness of meromorphic functions concerning small functions (Q2781339)

The author proved the following result: Two nonconstant meromorphic functions \(f\) and \(g\) in the complex field \(\mathbb{C}\) are equal if they satisfy NEWLINE\[NEWLINE\overline{E}_{f)k}(a_j)= \overline{E}_{g)k}(a_j),\qquad j=1,\dots,5,NEWLINE\]NEWLINE where \(a_1,\dots,a_5\) are distinct small functions with respect to \(f\) and \(g\), \(k\) is a positive integer with \(k\geq 14\), and \(\overline{E}_{f)k}(a_j)\) is the set of distinct zeros of \(f-a_j\) with multiplicities \(\leq k\). The case \(k=\infty\) was obtained by \textit{Li} and \textit{Qiao} [Adv. Math. (Chinese) 28 (1), 87--88 (1999)], which also is generalized by \textit{H. Yi} and \textit{Y. Li} [Chin. Ann. Math., Ser. A 22, No. 3, 271--278 (2001; Zbl 1107.30026)] and \textit{K. Ishizaki} [Arch. Math. 77, 273--277 (2001; Zbl 1093.30027)].