论文标题
新的广义互惠型功能方程的稳定性
Stability of a new generalized reciprocal type functional equation
论文作者
论文摘要
在本文中，我们研究了以下相互类型函数方程的广义hyers-ulam稳定性\ begin {equation*} f（2x+y）+f（2x-y）= \ frac {2f（x）f（x）f（y）\ sumsstyle \ sum _ {\ sum _ {\ sum _ { l} 2^{l-k} \ binom {l} {k} f（x）^{\ frac {k} {l}} {l}} f（y） ft（4f（y）^{\ frac {2} {l}} - f（x）^{\ frac {2} {l}} {l}} {l}} \ right）^l}在非零的真实和非架构空间中。
In this paper, we investigate the generalized Hyers-Ulam stability of the following reciprocal type functional equation \begin{equation*}f(2x+y)+f(2x-y)=\frac{2f(x)f(y)\displaystyle{\sum_{\substack{k=0\\ \text{$k$ is even}}}^{ l}2^{l-k}\binom{l}{k}f(x)^{\frac{k}{l}}f(y)^{\frac{l-k}{l}}}}{\left(4f(y)^{\frac{2}{l}}-f(x)^{\frac{2}{l}}\right)^l}\end{equation*} in non-zero real and non-Archimedean spaces.
