LAUSR

Using the fixed point theorem [12, Theorem 1] in (2, β)-Banach spaces, we prove the generalized hyperstability results of the bi-Jensen functional equation 4 f (x + z 2 , y + w 2 ) = f (x, y) + f (x,w) + f (z, y) + f (y,w). Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. The method we use here can be applied to various similar equations in many variables.