Biderivations and Bihomomorphisms in Banach Algebras

초록

In this paper, we solve the following bi-additive s-functional inequalities parallel to f(x+y, z+w) + f(x+y, z-w) + f(x-y, z+w) + f(x-y, z-w) - 4f(x, z)parallel to <= parallel to s(2f(x+y, z-w) + 2f(x-y, z+w) - 4f(x, z) + 4f(y, w)parallel to (1) and parallel to 2f(x+y, z-w) + 2f(x-y, z+w) - 4f(x, z) + 4f(y, w)parallel to (2) <=parallel to f(x+y, z+w) + f(x+y, z-w) + f(x-y, z+w) + f(x-y, z-w) - 4f(x, z)parallel to, where s is a fixed nonzero complex number with vertical bar s vertical bar < 1. Moreover, we prove the Hyers-Ulam stability of biderivations and bihomomorphismsions in Banach algebras and unital C*-algebras, associated with the bi-additive s-functional inequalities (1) and (2).

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