[PDF] Top 20 On the stability of the quadratic mapping in normed spaces

... for all x,y,z ∈ X and n ∈ N. Letting n tend toinfinity in the last inequality, then by (4.1) we obtain (1.3). Analogously, by (4.8), we can see that g is even. By substituting −y for z in (1.3) and by taking account of ... See full document

... the stability of the linear functional ...the stability of the linear mapping in Banach ...the stability of a quartic functional ...Hyers-Ulam-Rassias Stability of Functional Equations ... See full document

... Hyers-Ulam stability of multi- Euler-Lagrange quadratic functional equation ...fuzzy normed spaces over a field with valuation using the direct and the fixed point ... See full document

... the stability of the cubic functional equation f2x y f2x − y 2fx y 2fx − y 12fx in fuzzy normed spaces was proved in earlier work; and the stability of the additive functional equations fx y ... See full document

... multi-normed spaces, and investigate some properties of multi-bounded mappings on multi-normed ...Hyers–Ulam–Rassias stability theorem associated to the Cauchy additive equation for mappings ... See full document

... fuzzy normed spaces to fuzzy β -normed spaces and adopt the fixed point and direct methods to prove the Hyers-Ulam-Rassias stability of the quartic functional equation f (2x + y + z) + ... See full document

... metric spaces and L-fuzzy normed ...fuzzy normed spaces. On the other hand, the study of stability problems for a functional equation is related to the question of Ulam [] concerning ... See full document

... Recently, Alsina [18], Chang, et al. [19], Mirmostafaee et al. [20], [21], Miheţ and Radu [22], Miheţ et al. [23], [24], [25], [26], Baktash et al. [27], Eshaghi et al. [28], Saadati et al. [29], [30] investigated the ... See full document

... random normed spaces RN-spaces is important as a generalization of deterministic result of linear normed spaces and also in the study of random operator ...Hyers-Ulam stability ... See full document

... Hyers-Ulam-Rassias stability problem in quasi-β-normed spaces and then the stability by using a subadditive function for the generalized quartic function f : X → Y satisfying ... See full document

... Kim, “Generalized Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces,” Journal of Mathematical Analysis and Applications, vol.[r] ... See full document

... a quadratic functional ...the quadratic functional equation is said to be a quadratic ...Hyers-Ulam stability problem for the quadratic functional equation was proved by Skof [] for ... See full document

... f (2x + y) + f (2x − y) = 2f (x + y) + 2f (x − y) + 12f (x). (1 : 2) It is easy to show that the function f(x) = x 3 satisfies the functional equation (1.2), which is called a cubic functional equation and every solution ... See full document

... Type Quadratic functional ...Fuzzy stability of equation (1.3) and (1.4). The notion of a Random Normed space in which the values of the norms are probability distribution functions rather than ... See full document

... the stability of the linear transformation in Banach spaces, ...Fuzzy Stability of n-Dimensional Quadratic Functional Equation: Direct and Fixed Point Methods, ... See full document

... Theorem 5.2. Let K be a non-Archimedean field, X a vector space over K and (Y, P , T ) a non-Archimedean L-fuzzy Banach space over K. Let f : X → Y be a Ψ-approximately quadratic mapping. If there exist an ... See full document

... cubic mapping. The stability problem for the cubic functional equation was solved by Jun and Kim 2 and Lee 3 for mappings f : X → Y , where X is a real normed space and Y is a Banach ...the ... See full document

... The rest of the proof is similar to the proof of Theorem .. Corollary . Let θ be a positive real number and q is a real number with  < q < . Let f : X → Y be an odd mapping satisfying (.). Then there ... See full document

... Ulam [27] is the pioneer for the famous stability problem in functional equations. In 1940, while he was delivering a talk before the Mathematics Club of University of Wisconsin, he proposed a number of unsolved ... See full document

... a quadratic mapping. The Hyers-Ulam stability for quadratic functional equation was first proved by Skof [5] for mappings acting between a normed space and a Banach ...the normed ... See full document