Normal families of meromorphic functions concerning higher derivative and shared values (Q2015410)

Summary: We study normal families related to a conjecture of Hayman concerning shared values and get two normality criteria. Our results improve related theorems obtained independently by \textit{M.-L. Fang} and \textit{W.-J. Yuan} [Indian J. Math. 43, No. 3, 341--351 (2001; Zbl 1040.30015)], \textit{W.-J. Yuan} et al. [Discrete Dyn. Nat. Soc. 2011, Article ID 463287, 10 p. (2011; Zbl 1246.30066); Math. Methods Appl. Sci. 35, No. 17, 2095--2100 (2012; Zbl 1273.30023)], \textit{J.-H. Wang} et al. [Adv. Pure Math. 1, No. 4, 210--217 (2011; Zbl 1242.30029)] and \textit{B.-M. Deng} et al. Complex Var. Elliptic Equ. 59, No. 5, 616--630 (2014; Zbl 1291.30230)]. Also, some examples are given to show the sharpness of our results.