Research articles
ScienceAsia 47 (2021):ID 520-529 |doi:
10.2306/scienceasia1513-1874.2021.065
Meromorphic solutions of certain types of complex
functional equations
Zhi-Bo Huanga,*, Shuang-Ting Lanb, Ran-Ran Zhangc,*
ABSTRACT: In this paper, we investigate the properties of meromorphic solutions on complex functional equations of
Malmquist type of the form
XfJg
?J(z)‚Yj2J wqjzŒ = ba00((zz) + ) + ba11((zz)( )(ww?? pp) + ) +? ? ? ? ? ?++ abst((zz)( )(ww?? pp))st ,
where fJg is a collection of all non-empty subsets of f1,2, .. ., ng, q 2 C, jqj > 1, and all coefficients are small functions
relative to w(z) such that as(z)bt(z) 6? 0, p(z) = dkzk + ? ? ? + d1z + d0 is a polynomial with constant coefficients dk(6=
0), .. ., d1, d0 and of degree k. Furthermore, we prove that the meromorphic solutions having Borel exceptional zeros
and poles appear in special situations. Some other q-difference versions of complex difference equations of Malmquist
type are also presented.
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| a |
School of Mathematical Sciences, South China Normal University, Guangzhou 510631 China |
| b |
School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou
510665 China |
| c |
Department of Mathematics, Guangdong University of Education, Guangzhou 510303 China |
* Corresponding author, E-mail: huangzhibo@scnu.edu.cn, zhangranran@gdei.edu.cn
Received 3 Feb 2021, Accepted 26 Apr 2021
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