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In this paper, using fixed point method, we prove the Hyers-Ulam stability of the following functional equation \begin{eqnarray*} & &f(x+y+z)+f(\sigma(x)+y+z)+f(x+\sigma(y)+z)+f(x+y+\sigma(z))\\ &=&4f(x)+4f(y)+4f(z) \end{eqnarray*} with involution in paranormed spaces.

THE HYERS-ULAM STABILITY OF A QUADRATIC FUNCTIONAL EQUATION WITH INVOLUTION IN PARANORMED SPACES