Abstract
We present a method that allows to study approximate solutions to the two-variable Jensen functional equation $$\displaystyle 2f\Big (\frac {x+z}{2},\frac {y+w}{2}\Big )=f(x,y)+f(z,w) $$ on a restricted domain. Namely, we show that (under some weak natural assumptions) functions that satisfy the equation approximately (in some sense) must be actually solutions to it. The method is based on a quite recent fixed point theorem in some functions spaces and can be applied to various similar equations in many variables. Our outcomes are connected with the well-known issues of Ulam stability and hyperstability.
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