In this paper, we investigate approximate additive mappings, approximate Jensen mappings and approximate quadratic mappings in 2-Banach spaces. That is, we prove the generalized Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces.

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Abstract. In this paper, we prove the generalized Hyers-Ulam stability of bi-homomorphisms in C * -ternary algebras and of bi-derivations on C * -ternary algebras for the following bi-additive functional equationThis is applied to investigate bi-isomorphisms between C * -ternary algebras.

We prove the Hyers-Ulam-Rassias stability of the Jensen's equation in Banach modules over a Banach algebra.Let E 1 and E 2 be Banach spaces, and f :for all x; y 2 E 1 . Th.M. Rassias [7] showed that there exists a unique R-linear mapping T :The stability problems of functional equations have been investigated in several papers ([2, 3, 4, 5]).Throughout this paper, let B be a unital Banach algebra with norm j ¢ j, R + the set of positive real numbers, and B 1 the set of all elements of B having norm 1, and let B B 1 and B B 2 be left Banach B-modules with norms jj ¢ jj and k ¢ k, respectively.We are going to prove the Hyers-Ulam-Rassias stability of the Jensen's equation in Banach modules over a Banach algebra.

We find out the general solution of a generalized Cauchy-Jensen functional equation and prove its stability. In fact, we investigate the existence of a Cauchy-Jensen mapping related to the generalized Cauchy-Jensen functional equation and prove its uniqueness. In the last section of this paper, we treat a fixed point approach to the stability of the Cauchy-Jensen functional equation.