n this paper we study the Hyers-Ulam-Rassias stability of Cauchyequation in Felbin's type fuzzy normed linear spaces. As a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. This shows how the category offuzzy normed linear spaces differs from the classical normed linearspac...

Moslehian  and Mirmostafaee, investigated the fuzzystability problems for the Cauchy additive functional equation, the Jensen additivefunctional equation and the cubic functional equation in fuzzyBanach spaces. In this paper, we investigate thegeneralized Hyers–-Ulam--Rassias stability of the generalizedadditive functional equation with $n$--variables, in fuzzy Banachspaces. Also, we will show ...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

Let A be an algebra and let X be an A-bimodule. A C−linear mapping d : A → X is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ : A → X such that d(a) = ad(a) + δ(a)a for all a ∈ A. The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.

We prove generalized Hyres-Ulam-Rassias stability of the cubic functional equation f(kx + y) + f(kx − y) = k[f(x + y) + f(x − y)] + 2(k − k)f(x) for all k ∈ N and the quartic functional equation f(kx + y) + f(kx − y) = k[f(x + y) + f(x − y)] + 2k(k − 1)f(x)− 2(k − 1)f(y) for all k ∈ N in non-Archimedean normed spaces.

We use the fixed point method to prove the probabilistic Hyers–Ulam and generalized Hyers–Ulam–Rassias stability for the nonlinear equation f (x) = Φ(x, f (η(x))) where the unknown is a mapping f from a nonempty set S to a probabilistic metric space (X ,F,TM) and Φ : S×X → X , η : S → X are two given functions. Mathematics subject classification (2000): 39B52, 39B82, 47H10, 54E70.

In this paper, we investigate the exact and approximate controllability, finite time stability, β–Hyers–Ulam–Rassias stability of a fractional order neutral impulsive differential system. The controllability criteria is incorporated with help fixed point approach. famous generalized Grönwall inequality used to study stability. Finally, main results are verified an example.

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of nonArchimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-...

We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism f from a Banach algebra into a semisimple commutative...

In this paper, we introduce the following additive type functional equation f(rx+ sy) = r + s 2 f(x+ y) + r − s 2 f(x− y), where r, s ∈ R with r + s, r − s 6= 0. Also we investigate the Hyers–Ulam–Rassias stability of this functional equation in Banach modules over a unital C∗-algebra. These results are applied to investigate homomorphisms between C∗-algebras. 2000 Mathematics Subject Classific...