No abstract

We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.If we substitute those expressions for x, y, z, w in the second one and if we carry out a tedious calculation, then we get a quadratic equationThis equation has one solution α which is not less than 0 and −d because of q(0) ≤ 0 and q(−d) = −(a 2 + c 2 − 2bd) 2 ≤ 0. Thus, the system is solvable in R 4 for d = 0.In the following theorem, we investigate the solutions of the functional equation (4) by the same idea that was applied to the proof of Theorem 1.

No abstract

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.