growth of meromorphic solutions for complex difference‎ ‎equations of malmquist type

نویسندگان

y‎. ‎y‎. zhang

lmib & school of mathematics and systems science‎, ‎beihang university‎, ‎beijing‎, ‎100191‎, ‎china. z. s. gao

lmib & school of mathematics and systems science‎, ‎beihang university‎, ‎beijing‎, ‎100191‎, ‎china. j. l. zhang

lmib & school of mathematics and systems science‎, ‎beihang university‎, ‎beijing‎, ‎100191‎, ‎china.

چکیده

‎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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bulletin of the iranian mathematical society

جلد ۴۲، شماره ۶، صفحات ۱۴۹۷-۱۵۰۵

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