We prove the generalized Hyers-Ulam stability of the following quadratic functional equations and in fuzzy Banach spaces for a nonzero real number with .

No abstract

In [40], Th.M. Rassias introduced the following equality, then the mapping f : V → W is realized as the sum of an additive mapping and a quadratic mapping. From the above equality we can define the functional equationwhich is called a quadratic functional equation. Every solution of the quadratic functional equation is said to be a quadratic mapping.Using fixed point theorem we prove the Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.

The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations f x y f x −y 2f x 2f y and f ax by f ax −by 2a 2 f x 2b 2 f y a, b ∈ R\{0}, a / ± 1 in fuzzy Banach spaces.

Abstract. If the Wiener-Hopf C * -algebra W(G, M ) for a discrete group G with a semigroup M has the uniqueness property, then the structure of it is to some extent independent of the choice of isometries on a Hilbert space. In this paper we show that if the Wiener-Hopf C * -algebra W(G, M ) of a partially ordered group G with the positive cone M has the uniqueness property, then (G, M ) is weakly unperforated. We also prove that the Wiener-Hopf C * -algebra W(Z, M ) of subsemigroup M generating the integer group Z is isomorphic to the Toeplitz algebra, but W(Z, M ) does not have the uniqueness property except the case M = N.