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We solve the bi-additive functional equation f(x+y,z−w)+f(x−y,z+w)=2f(x,z)−2f(y,w) and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unital C⋆-algebra

discrete dynamics in nature and society

Stability of a Bi-Additive Functional Equation in Banach Modules Over a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mi>C</mml:mi><mml:mo>⋆</mml:mo></mml:msup></mml:mrow></mml:math>-Algebra

Stability of a Bi-Additive Functional Equation in Banach Modules Over aC⋆-Algebra