Abstract
In this paper, we prove the stability of the following functional equation ∑ i = 0 n n C i ( − 1 ) n − i f ( i x + y ) − n ! f ( x ) = 0 on a restricted domain by employing the direct method in the sense of Hyers.
Highlights
Let V and W be real vector spaces, X a real normed space, Y a real Banach space, n ∈ N (the set of natural numbers), and f : V → W a given mapping
Let V and W be real vector spaces, X a real normed space, Y a real Banach space, n ∈ N, and f : V → W a given mapping
In this paper, we prove the stability of the following functional equation
Summary
Let V and W be real vector spaces, X a real normed space, Y a real Banach space, n ∈ N (the set of natural numbers), and f : V → W a given mapping. There exist a positive real number K and a unique monomial function of degree n (Corollary 4 in [7]) A mapping f : V → W is a solution of the functional Equation (1) if and only if f is of the form f ( x ) = An ( x ) for all x ∈ V, where An is the diagonal of the n-additive symmetric mapping An : V n → W.
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