Stability of a quadratic Jensen type functional equation in the spaces of generalized functions

Making use of the fundamental solution of the heat equation we find the solution and prove the stability theorem of the quadratic Jensen type functional equation 9f x + y + z 3 +f (x) +f (y)+f (z) = 4 f x + y 2 +f y +z 2 + f z + x 2 in the spaces of Schwartz tempered distributions and Fourier hyperfunctions. © 2006 Elsevier Inc. All rights reserved.