1LMIB and School of Mathematics & Systems Science Beihang University Beijing, 100191, P.R. China 2Beihang University LMIB and School of Mathematics & Systems Science Beijing, 100191, P.R. China 3College of Science Guangdong Ocean University Zhanjiang, Guangdong, 524008, P.R. China
Annales Polonici Mathematici, Tome 102 (2011) no. 3, pp. 213-221
We investigate the distribution of zeros and shared values of the difference operator on meromorphic functions. In particular, we show that if $f$ is a transcendental meromorphic function of finite order with a small number of poles, $c$ is a non-zero complex constant such that $\Delta ^k_cf\not =0$ for $n\geq 2$, and $a$ is a small function with respect to $f$, then $f^n\Delta ^k_cf$ equals $a$$(\not =0, \infty )$ at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved.
Keywords:
investigate distribution zeros shared values difference operator meromorphic functions particular transcendental meromorphic function finite order small number poles non zero complex constant delta geq small function respect delta equals infty infinitely many points uniqueness difference polynomials points fixed points proved
Affiliations des auteurs :
Jilong Zhang
1
;
Zongsheng Gao
2
;
Sheng Li
3
1
LMIB and School of Mathematics & Systems Science Beihang University Beijing, 100191, P.R. China
2
Beihang University LMIB and School of Mathematics & Systems Science Beijing, 100191, P.R. China
3
College of Science Guangdong Ocean University Zhanjiang, Guangdong, 524008, P.R. China
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title = {Distribution of zeros and shared values of
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Jilong Zhang; Zongsheng Gao; Sheng Li. Distribution of zeros and shared values of
difference operators. Annales Polonici Mathematici, Tome 102 (2011) no. 3, pp. 213-221. doi: 10.4064/ap102-3-2
