Asymptotic behavior of generalized quadratic mappings

Document Type : Research Paper


1 Department of Mathematics, Chungnam National University 99 Daehangno, Yuseong-gu, Daejeon 305-764, Korea

2 Department of Mathematics, Chungnam National University, 99 Daehangno, Yuseong-gu, Daejeon 34134, Korea


We show in this paper that a mapping $f$ satisfies the following functional equation
\biguplus_{x_2,\cdots,x_{d+1}}^{d}f(x_1) = 2^{d} \sum_{i=1}^{d+1}f(x_i),
if and only if it is quadratic. In addition, we investigate generalized Hyers-Ulam stability problem for the equation, and thus obtain an asymptotic property of quadratic mappings as applications.


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Volume 12, Issue 1
May 2021
Pages 1153-1165
  • Receive Date: 09 February 2021
  • Revise Date: 05 March 2021
  • Accept Date: 13 March 2021