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Ulam stability of bihomomorphisms and biderivations in Banach algebras
Journal of Fixed Point Theory and Applications ( IF 1.4 ) Pub Date : 2020-03-12 , DOI: 10.1007/s11784-020-0766-z
Choonkil Park , Siriluk Paokanta , Raweerote Suparatulatorn

Using the fixed point method and the direct method, we prove the Hyers–Ulam stability of biderivations and bihomomorphisms in Banach algebras and unital \(C^*\)-algebras, associated with the bi-additive functional inequality:$$\begin{aligned}&\Vert f(x+y, z+w) + f(x+y, z-w) + f(x-y, z+w) \nonumber \\&\quad + f(x-y, z-w) -4f(x,z)\Vert \nonumber \\&\quad \le \left\| s \left( 2f\left( x+y, z-w\right) + 2f\left( x-y, z+w\right) - 4f(x,z )+ 4 f(y, w)\right) \right\| , \end{aligned}$$(1)where s is a fixed nonzero complex number with \(|s |< 1\).

中文翻译:

Banach代数中双同态和除态的Ulam稳定性

使用固定点法和直接法中,我们证明在Banach代数和酉biderivations和bihomomorphisms的Hyers-乌拉姆稳定性\(C ^ * \) -代数,与双官能添加剂相关的不等式:$$ \ {开始对齐}&\ Vert f(x + y,z + w)+ f(x + y,zw)+ f(xy,z + w)\ nonumber \\&\ quad + f(xy,zw)-4f( x,z)\ Vert \ nonumber \\&\ quad \ le \ left \ | s \ left(2f \ left(x + y,zw \ right)+ 2f \ left(xy,z + w \ right)-4f(x,z)+ 4 f(y,w)\ right)\ right \ | ,\ end {aligned} $$(1),其中s是带有\(| s | <1 \)的固定非零复数。
更新日期:2020-03-12
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