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We generalize the results obtained by Jun and Min (2009) and use fixed point method to obtain the stability of the functional equationf(x+σ(y))=F[f(x),f(y)], for a class of functions of a vector space into a Banach space whereσis an involution. Then we obtain the stability of the differential equations of the formy′=F[q(x),P(x)y(x)].doi:10.1155/2011/128479 fatcat:p45xi3n2xjehtjkxrtn6a3xk6i