Ulam stability of bihomomorphisms and biderivations in Banach algebras

Abstract

© 2020, Springer Nature Switzerland AG. 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: ‖f(x+y,z+w)+f(x+y,z-w)+f(x-y,z+w)+f(x-y,z-w)-4f(x,z)‖≤∥s(2f(x+y,z-w)+2f(x-y,z+w)-4f(x,z)+4f(y,w))∥,where s is a fixed nonzero complex number with | s| < 1.