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1

Meromorphic solutions of q-shift difference equations

100%

Liu K., Qi X.-G.

Annales Polonici Mathematici

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2011

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tom 101

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nr 3

215-225

EN

We establish a q-shift difference analogue of the logarithmic derivative lemma. We also investigate the value distributions of q-shift difference polynomials and the growth of solutions of complex q-shift difference equations.

2

Differential analogues of the Brück conjecture

100%

Qi X.-G., Yang L.-Z.

Annales Polonici Mathematici

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2011

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tom 101

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nr 1

31-38

EN

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.

3

Uniqueness of entire functions and fixed points

100%

Qi X.-G., Yang L.-Z.

Annales Polonici Mathematici

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2010

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tom 97

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nr 1

87-100

EN

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 $(fⁿ(z)(λf^m(z)+μ))^(k)$ must have infinitely many fixed points if n ≥ k + 2; furthermore, if $(fⁿ(z)(λf^m(z)+μ))^(k)$ and $(gⁿ(z)(λg^m(z)+μ))^(k)$ 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.

Ograniczanie wyników

3 Annales Polonici Mathematici

3 Qi X.-G.

2 Yang L.-Z.

1 Liu K.

2 2011

1 2010

Meromorphic solutions of q-shift difference equations

Differential analogues of the Brück conjecture

Uniqueness of entire functions and fixed points