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...