Abstract. Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X to Y , which satisfies the inequality || Delta ^n_x f(y) − n!f(x)|| < gi(x, y) for suitable control function g 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 to f(tx) and t to g (tx, ty) imply the continuity of t to M(tx).

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