The purpose of this paper is twofold. The first is to weaken or omit the condition for i ≠ j in some previous uniqueness theorems for meromorphic mappings. The second is to decrease the number q of hyperplanes such that f(z) = g(z) on , where f,g are meromorphic mappings.
Applying the normal family theory and the theory of complex differential equations, we obtain a uniqueness theorem for entire functions that share a function with their first and second derivative, which generalizes several related results of G. Jank, E. Mues & L. Volkmann (1986), C. M. Chang & M. L. Fang (2002) and I. Lahiri & G. K. Ghosh (2009).
We use the theory of normal families to obtain some uniqueness theorems for entire functions, which improve and generalize the related results of Rubel and Yang, and Li and Yi. Some examples are provided to show the sharpness of our results.
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