巴拿赫代数中的置换三同态和置换三同态( Permuting triderivations and permuting trihomomorphisms in Banach algebras )

C Park Y Jin YS Dong X Zhang V Govindan

本文解决了以下三加性s-泛函不等式egin{eqnarray}label{0.1}&onumberf(x+y,z-w,a+b)+f(x-y,z+w,a-b)\&onumberqquad-2f(x,z,a)+2f(x,w,b)-2f(y,z,b)+2f(y,w,a)\&quadleftsleft(2fleftfleft(frac{x+y}{2},z-w,a+b ight)+2fleft(frac{x+y}{2},z-w,a+b ight)+2fleft(frac{x-y}{2},z+w,a+b ight).轻点。\&qquad左。左。-2 f（x,z,a）+2 f（x,w,b）-2 f（x,w,b）+2 f（y,w,a）轻,onumber结束{eqnarray}开始{eqnarray}标签{0.1}&onumberf（x+y,z-w,a+b）+f（x,z,a）+2 f（x,w,b）-2f（y,z,b）+2 f（y,w,a）\\&四lefsleft(2fleft(frac{x+y}{2},z）-w,a+b光）+2f左(FRAC{x-y}{2},z+w,a-光）光。轻点。\&qquad左。左。-2 f（x,z,a）+2 f（x,w,b）-2f（y,z,b）+2 f（y,w,a）轻点,onumber结束{eqnarray}开始{eqnarray}标签{0.2}&onumber左2fleft(frac{x+y}{2},z-w,a+b轻点）+2fleft(frac{x+y}{2},z+w,a-bight）轻点。\&&onumberqquadleft。-2 f(x,z,a)+2 f(x,w,b)-2f(y,z,b)+2f(y,w,a）轻\&四les(f(x+y,z-w,a+b)+f(x-y,z+w,a-b)\&onumberqquad-2 f(x,z,a)+2 f(x,w,b)-2f(y,z,b)+2f(y,w,a))\结束{eqnarray}开始{eqnarray}标签{0.2}&onumberleftfrac{x+y}{2},z-w,a+b右）+2f左(frac{x-y}{2},z+w,a-bight）右。\&&onumberqquadleft。-2 f（x,z,a)+2 f（x,w,b)-2f（y,z,b)+2 f（y,w,a）轻\&四les(f(x+y,z-w,a+b)+f(x-y,z+w,a-b)\&一个数字q四-2 f（x,z,a)+2 f（x,w,b)-2f(y,z,b)+2 f（y,w,b))\end{eqnarray}其中s<1s<1的固定非零复数。此外,我们证明了Banach代数和单元C^*C^*-代数中置换三导子和置换三同态的Hyers-Ulam稳定性和超稳定性,并与三可加s s-泛函不等式{m（ef{0.1}ef{0.1}）}和{m（ef{0.2}ef{0.2}）}联系起来。

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