Displaying similar documents to “Some applications of Nevanlinna theory to entire functions that share a small function with two difference operators”

Entire functions that share values or small functions with their derivatives

Sheng Li, Zongsheng Gao, Jilong Zhang (2012)

Annales Polonici Mathematici

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We investigate the uniqueness of entire functions sharing values or small functions with their derivatives. One of our results gives a necessary condition on the Nevanlinna deficiency of the entire function f sharing one nonzero finite value CM with its derivative f'. Some applications of this result are provided. Finally, we prove some further results on small function sharing.

Entire functions that share a function with their first and second derivatives

Feng Lü, Junfeng Xu (2012)

Annales Polonici Mathematici

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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).

Uniqueness theorems for entire functions whose difference polynomials share a meromorphic function of a smaller order

Xiao-Min Li, Wen-Li Li, Hong-Xun Yi, Zhi-Tao Wen (2011)

Annales Polonici Mathematici

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We deal with uniqueness of entire functions whose difference polynomials share a nonzero polynomial CM, which corresponds to Theorem 2 of I. Laine and C. C. Yang [Proc. Japan Acad. Ser. A 83 (2007), 148-151] and Theorem 1.2 of K. Liu and L. Z. Yang [Arch. Math. 92 (2009), 270-278]. We also deal with uniqueness of entire functions whose difference polynomials share a meromorphic function of a smaller order, improving Theorem 5 of J. L. Zhang [J. Math. Anal. Appl. 367 (2010), 401-408],...

Uniqueness theorems and normal families of entire functions and their derivatives

Feng Lü, Junfeng Xu, Hongxun Yi (2009)

Annales Polonici Mathematici

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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.