Normality criteria involving differential polynomials

In this paper, we prove normality criteria for families of meromorphic functions involving sharing of a holomorphic function by a certain class of differential polynomials. Results in this paper extend the works of different authors carried out in recent years, for example Charak and Sharma (Turk J Math 41: 404–411, 2017), Fang and Yuan (J Aust Math Soc Ser A 68(3): 321–333, 2000) Jiang and Gao (Acta Math Sci 32(4): 1503–1512, 2012), Meng and Hu (Bull Malays Math Sci Soc 38:1331–1347, 2015), Sun (Kragujev J Math 38(2):273–282, 2014), Xiao et al. (Abstr Appl Anal Article ID 373910, 1–8, 2011), Yuan (Arch Math 96(5): 435–444 2011).