We study the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share the same simple and double $1$-points and improve an earlier result given by Fang-Fang and a recent result of Lahiri-Mandal.
"A uniqueness result on some differential polynomials sharing 1-points." Hiroshima Math. J. 37 (3) 397 - 408, November 2007. https://doi.org/10.32917/hmj/1200529810