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In this paper, a generalized Hyers-Ulam stability of the homogeneous equation shall be proved, i.e., if a mapping f satisfies the functional inequality ‖f(yx)−ykf(x)‖≤φ(x,y) under suitable conditions, there exists a unique mapping T satisfying T(yx)=ytT(x) and ‖T(x)−f(x)‖≤Φ(x).