On the quadratic functional equation modulo a subgroup

Abstract

Let X be a topological vector space, let Y be a topological Abelian group, and let K be a discrete subgroup of Y. Assunme that a function f: X -> Y satisfies (2) for all x, y is an element of X. We will prove that if f is continuous at the origin, then there exists a quadratic function allowed to deviate from f (x) - f (0) within K.