On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

The Hyers-Ulam stability problems of functional equations go back to 1940 when S. M. Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group see 1 . A partial answer was given by Hyers et al. 2, 3 under the assumption that the target space of the involved mappings is a Banach space. After the result of Hyers, Aoki 4 , and Bourgin 5, 6 dealt with this problem, however, there were no other results on this problem until 1978 when Rassias 7 dealt again with the inequality of Aoki 4 . Following the Rassias’ result, a great number of papers on the subject have been published concerning numerous functional equations in various directions 2, 7–21 . The following four functional equations are called trigonometric functional equations.