论文标题
在复杂的Banach代数中置换三个三角形和置换的三角形
Permuting triderivations and permuting trihomomorphisms in complex Banach algebras
论文作者
论文摘要
在本文中，我们解决了以下三级$ s $ s $功能不平等\ begin {eqnarray} \ label {0.1} && \ nonumber \ | f（x +y，z-w，a +b） +f（x-y，z +w，a-b）\\ && \ nonumber \ qquad \ qquad -2 f（x，z，z，a） +2 f（x，x，w，w，w，b）-2f（y，z，z，z，z，z，b）+2 f（y，w（y，w，w，a） \\ && \ quad \ le \ lest \ | s \ lesg（2f \ left（\ frac {x+y} {2} {2}，z-w，z-w，a+b \ right）+2f \ left（\ frac {x-y} {x-y} {2} {2} {2} {2}，z+w，z+w，z+w，a-b \ right）\左右。 f（x，z，a） + 2 f（x，w，b）-2f（y，z，b）+2 f（y，w，a）\ right）\ right \ | ，\ nonumber \ end {eqnArray} \ begin {eqnarray} \ label {0.2} && \ nonumber \ left \ left \ | 2f \ | 2f \ left（\ frac {x+y} {2} {2} {2} {2 a-b \ right）\ right。 \\ && \ nonumber \ qquad \ left。 -2 f（x，z，a） + 2 f（x，w，b）-2f（y，z，b）+2 f（y，w，a）\ right \ | \\ && \ quad \ le \ | s（f（x +y，z-w，a +b） +f（x-y，z +w，a-b）\\ && \ nonumber \ ququad \ qquad -2 f（x，z，z，a） +2 f（x，x，x，x，x，x，w，w，w，w，w，b）-2f（y，z，z，z，z，z，z，z，z，z，b）+2 f（y，w，y，a） ，\ end {eqnarray}，其中$ s $是固定的非零复数，带有$ | s | <1 $。此外，我们证明了Hyers-ulam的稳定性和置于Banach代数和UNITAL $ C^*$ - 代数的置换和置换三态的稳定性，并与三效$ s $ s $ s $ s $ s $ s $ s-功能不平等相关的代数{
In this paper, we solve the following tri-additive $s$-functional inequalities \begin{eqnarray}\label{0.1} && \nonumber \| f(x+y, z-w, a+b) + f(x-y, z+w, a-b) \\ && \nonumber\qquad -2 f(x, z, a) + 2 f(x, w, b) -2f(y, z, b) +2 f(y, w, a)\| \\ && \quad \le \left \|s \left(2f\left(\frac{x+y}{2}, z-w, a+b \right) + 2f\left(\frac{x-y}{2}, z+w, a-b\right) \right. \right. \\ && \qquad \left. \left. -2 f(x, z, a) + 2 f(x, w, b) -2f(y, z, b) +2 f(y, w, a)\right)\right\| , \nonumber \end{eqnarray} \begin{eqnarray}\label{0.2} && \nonumber \left\|2f\left(\frac{x+y}{2}, z-w, a+b \right) + 2f\left(\frac{x-y}{2}, z+w, a-b\right) \right. \\ && \nonumber \qquad \left. -2 f(x, z, a) + 2 f(x, w, b) -2f(y, z, b) +2 f(y, w, a)\right\| \\ && \quad \le \|s ( f(x+y, z-w, a+b) + f(x-y, z+w, a-b) \\ && \nonumber\qquad -2 f(x, z, a) + 2 f(x, w, b) -2f(y, z, b) +2 f(y, w, a) )\| , \end{eqnarray} where $s$ is a fixed nonzero complex number with $|s |< 1$. Moreover, we prove the Hyers-Ulam stability and hyperstability of permuting triderivations and permuting trihomomorphisms in Banach algebras and unital $C^*$-algebras, associated with the tri-additive $s$-functional inequalities {\rm (\ref{0.1})} and {\rm (\ref{0.2})}.
