In this paper, we investigate the generalized Hyers-Ulam stability problem of a quadratic and additive type functional equation f n i=1 x i + (n − 2) n i=1 f (x i) = 1i<jn f (x i + x j), (n > 2) for the even or odd case in the n variables. The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, J.
In the present paper, we investigate the situations so that the generalized Hyers-Ulam-Rassias stability for functional equations f(x 2) = f(x)x + xf(x) and f(xy) = f(x)y + xf(y) is satisfied. As a result we obtain that every linear mapping on a commutative Banach algebra which is an ε-approximate derivation maps the algebra into its radical.
In this article, we prove the generalized Hyers–Ulam stability of the following Cauchy additive functional equation f x − y n + z + f y − z n + x + f z − x n + y = f (x + y + z) in fuzzy Banach spaces for any fixed nonzero integer n. A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull.
In this paper, we investigate homomorphisms from unital C * − algebras to unital Ba-nach algebras and derivations from unital C * − algebras to Banach A− modules related to a Cauchy–Jensen functional inequality.
we establish the general solution for a mixed type functional equation of aquartic and a quadratic mapping in linear spaces. In addition, we investigate the generalized Hyers-Ulam stability in p-Banach spaces.