Meromorphic functions and also their first two derivatives have the same zeros.
Some results related to a conjecture of R. Brück concerning meromorphic functions sharing one small function with their derivaties.
Meromorphic functions that share one value with their derivatives.
Some results related to a conjecture of R. Brück.
Entire functions that share fixed-points.
Uniqueness of entire functions and fixed points
Let f and g be entire functions, n, k and m be positive integers, and λ, μ be complex numbers with |λ| + |μ| ≠ 0. We prove that must have infinitely many fixed points if n ≥ k + 2; furthermore, if and have the same fixed points with the same multiplicities, then either f ≡ cg for a constant c, or f and g assume certain forms provided that n > 2k + m* + 4, where m* is an integer that depends only on λ.
Differential analogues of the Brück conjecture
We give some growth properties for solutions of linear complex differential equations which are closely related to the Brück Conjecture. We also prove that the Brück Conjecture holds when certain proximity functions are relatively small.
The zero distribution and uniqueness of difference-differential polynomials
We consider the zero distribution of difference-differential polynomials of meromorphic functions and present some results which can be seen as the discrete analogues of the Hayman conjecture. In addition, we also investigate the uniqueness of difference-differential polynomials of entire functions sharing one common value. Our theorems improve some results of Luo and Lin [J. Math. Anal. Appl. 377 (2011), 441-449] and Liu, Liu and Cao [Appl. Math. J. Chinese Univ. 27 (2012), 94-104].
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