We introduce the injective tensor products and the projective tensor products of ordered vector spaces with Archimedean order unit and study their functorial properties. The local characterization of a nuclear space is given.

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

For a Köthe sequence space, the classes of Λ0-nuclear spaces and spaces with the Λ0-property are introduced and studied and the relation between them is investigated. Also, we show that, for Λ0 6= c0, these classes of spaces are in general different from the corresponding ones for Λ0 = c0, which have been extensively studied in the non-archimedean literature (see, for example, [1]–[6]).

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functional equation f(x+ y) + f(x− y) = 2f(x) + 2f(y) in non-Archimedean L-fuzzy normed spaces.

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.