Ulam stability problem for quadratic mappings of Euler-Lagrange

The purpose of this paper is to solve the stability problem of Ulam for an approximate mapping f:A→B of the following quadratic functional equation of Euler-Lagrange(a+b)aQ(x)+(a+b)bQ(y)=Q(ax+by)+abQ(x-y)for all x,y∈A with A and B linear spaces.