On the Ulam stability of the Cauchy-Jensen equation and the additive-quadratic equation

In this paper, we investigate the Ulam stability of the functional equations \[2f ( x + y; \frac{z + w}{ 2} ) = f(x; z) + f(x;w) + f(y; z) + f(y;w)\]and\[f(x + y; z + w) + f(x + y; z w) = 2f(x; z) + 2f(x;w) + 2f(y; z) + 2f(y;w)\] in paranormed spaces.