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Volume 47 Number 5
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Volume 47 Number 4 Volume 47 Number 5

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Research articles

ScienceAsia 47 (2021): 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 wqjz = 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