Stability of the Monomial Functional Equation in Quasi Normed Spaces
نویسندگان
چکیده
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 ||∆xf(y)− n!f(x)|| ≤ φ(x, y) for suitable control function φ, 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 7→ f(tx) and t 7→ φ(tx, ty) imply the continuity of t 7→ M(tx).
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