In this paper, the nonlinear stability of a functional equation in the setting of non-Archimedean normed spaces is proved. Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the and the theory of functional equations are also presented Key word: Hyers Ulam Rassias stability • cubic mappings • generalized normed space • Banach spac...

As is well known, equations of degree up to 4 can be solved in radicals . The solutions can be obtained, apart from the usual arithmetic operations, by the extraction of roots. In the case of the quadratic equation, this has a very concrete meaning. Even if the coefficients are arbitrary complex numbers, the solutions can always be calculated by the extraction of roots from nonnegative real num...

In this paper, we investigate the generalizedHyers--Ulam stability of the functional equation