Solutions of the n th-order Cauchy difference equation on groups

Advances in Difference Equations

Bolin Ma¹  Lin Li¹  Qiaoling Guo¹ 

[1] College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, P.R. China

关键词: Cauchy difference;    free group;    symmetric group;    cyclic group;    39B52;    39A70;   

DOI  :  10.1186/s13662-015-0700-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Let(G,⋅)$(G, \cdot)$be a group,(H,+)$(H, +)$be an Abelian group, andf:G→H$f:G\rightarrow H$be a function. In this paper, for a positive integer n, we first give a representation of nth-order Cauchy difference of f via the function asC(n)f(x1,x2,…,xn,xn+1)=∑1≤m≤n+1(−1)n+1−m∑1≤i1

【 授权许可】

CC BY