Ulam stability of bihomomorphisms and biderivations in Banach algebras

• DOI: 10.1007/s11784-020-0766-z
• Publication Date: 2020-03-12T10:02:33Z
• Authors: Choonkil Park; Siriluk Paokanta; Raweerote Suparat...
• Keywords: Unital; Banach algebra

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: 1$$\begin{aligned}&\Vert f(x+y, z+w) + f(x+y, z-w) + f(x-y, z+w) \nonumber \\&\quad + f(x-y, z-w) -4f(x,z)\Vert \nonumber \\&\quad \le \left\| s \left( 2f\left( x+y, z-w\right) + 2f\left( x-y, z+w\right) - 4f(x,z )+ 4 f(y, w)\right) \right\| , \end{aligned}$$where s is a fixed nonzero complex number with $$|s |< 1$$.