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We investigate the uniqueness problem of entire functions that share two polynomials with their th derivatives and obtain some results which improve and generalize the recent result due to Lü and Yi (2011). Also, we exhibit some examples to show that the conditions of our results are the best possible.
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).
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