Some further results on weighted sharing three values and Brosch’s theorem

Using the notion of weighted sharing of values we prove two uniqueness theorems which improve the results proved by T.C. Alzahary [T.C. Alzahary, Weighted sharing three values and Brosch’s theorem. J. Math. Anal. Appl. 323 (2006) 8–25; T.C. Alzahary, On a result of Ueda concerning unicity of meromorphic functions. Kodai. Math. J. 30 (2007) 140–146], under a weaker hypothesis.