Displaying similar documents to “Results on the deficiencies of some differential-difference polynomials of meromorphic functions”

The fixed points and iterated order of some differential polynomials

Benharrat Belaidi (2009)

Commentationes Mathematicae Universitatis Carolinae

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This paper is devoted to considering the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation f ' ' + A 1 ( z ) f ' + A 0 ( z ) f = F , where A 1 ( z ) , A 0 ( z ) ( ¬ ≡ 0 ) , F are meromorphic functions of finite iterated p -order.

Some properties of solutions of complex q-shift difference equations

Hong-Yan Xu, Jin Tu, Xiu-Min Zheng (2013)

Annales Polonici Mathematici

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Combining difference and q-difference equations, we study the properties of meromorphic solutions of q-shift difference equations from the point of view of value distribution. We obtain lower bounds for the Nevanlinna lower order for meromorphic solutions of such equations. Our results improve and extend previous theorems by Zheng and Chen and by Liu and Qi. Some examples are also given to illustrate our results.

Meromorphic solutions of q-shift difference equations

Kai Liu, Xiao-Guang Qi (2011)

Annales Polonici Mathematici

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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.

Fixed points of meromorphic functions and of their differences and shifts

Zong-Xuan Chen (2013)

Annales Polonici Mathematici

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Let f(z) be a finite order transcendental meromorphic function such that λ(1/f(z)) < σ(f(z)), and let c ∈ ℂ∖0 be a constant such that f(z+c) ≢ f(z) + c. We mainly prove that m a x τ ( f ( z ) ) , τ ( Δ c f ( z ) ) = m a x τ ( f ( z ) ) , τ ( f ( z + c ) ) = m a x τ ( Δ c f ( z ) ) , τ ( f ( z + c ) ) = σ ( f ( z ) ) , where τ(g(z)) denotes the exponent of convergence of fixed points of the meromorphic function g(z), and σ(g(z)) denotes the order of growth of g(z).