### Meromorphic solutions of some complex difference equations.

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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 $max\tau \left(f\left(z\right)\right),\tau \left({\Delta}_{c}f\left(z\right)\right)=max\tau \left(f\right(z\left)\right),\tau \left(f\right(z+c\left)\right)=max\tau \left({\Delta}_{c}f\left(z\right)\right),\tau \left(f(z+c)\right)=\sigma \left(f\left(z\right)\right)$, 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).

We investigate the growth and Borel exceptional values of meromorphic solutions of the Riccati differential equation w' = a(z) + b(z)w + w², where a(z) and b(z) are meromorphic functions. In particular, we correct a result of E. Hille [Ordinary Differential Equations in the Complex Domain, 1976] and get a precise estimate on the growth order of the transcendental meromorphic solution w(z); and if at least one of a(z) and b(z) is non-constant, then we show that w(z)...

Let $f$ be a transcendental meromorphic function. We propose a number of results concerning zeros and fixed points of the difference $g\left(z\right)=f(z+c)-f\left(z\right)$ and the divided difference $g\left(z\right)/f\left(z\right)$.

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