# Growth of meromorphic solutions for complex difference‎ ‎equations of Malmquist type

Document Type : Research Paper

Authors

LMIB & School of Mathematics and Systems Science‎, ‎Beihang University‎, ‎Beijing‎, ‎100191‎, ‎China.

Abstract

‎In this paper‎, ‎we give some necessary conditions for a complex‎ ‎difference equation of Malmquist type‎
$$‎\sum^n_{j=1}f(z+c_j)=\frac{P(f(z))}{Q(f(z))}‎,$$
‎where $n(\in{\mathbb{N}})\geq{2}$‎, ‎and $P(f(z))$ and $Q(f(z))$ are‎ ‎relatively prime polynomials in $f(z)$ with small functions as‎ ‎coefficients‎, ‎admitting a meromorphic function of finite order‎. ‎Moreover‎, ‎the properties of finite order transcendental meromorphic‎ ‎solutions for complex difference equation‎ ‎$\prod^n_{j=1}f(z+c_j)=P(f(z))/Q(f(z))$ are also investigated.

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Main Subjects

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### History

• Receive Date: 27 April 2014
• Revise Date: 22 September 2015
• Accept Date: 23 September 2015