STABILITY OF THE MONOMIAL FUNCTIONAL EQUATION IN QUASI NORMED SPACES

Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X -> Y, which satisfies the inequality vertical bar vertical bar Delta(n)(x)f(y) - n!f(x)vertical bar vertical bar <= phi(x, y) for suitable control function phi, there is a unique monomial function M of degree n which is a good approximation for f in such a way that the continuity of t bar right arrow f(tx) and t bar right arrow phi(tx, ty) imply the continuity of t bar right arrow M(tx).