Orthogonal stability of the Cauchy equation on balls

Abstract

We deal with stability of some functional equations postulated for orthogonal vectors in a ball centered at the origin. The maps considered are defined on a finite dimensional inner product space and take their values in a real sequentially complete linear topological space. The main result establishes the stability of the corresponding conditional Cauchy functional equation and as a consequence we obtain some other stability results. Results which do not involve the orthogonality relation are considered in more general structures.