[PDF] Top 20 3 Dimensional Additive Quadratic Functional Equation

... for functional equations is related to a question of Ulam [51] concerning the stability of group homomorphisms was affirmatively answered for Banach spaces by Hyers ...for additive mappings and by Rassias ... See full document

... cx 3 is a solution of the functional equation ...mixed functional equations has recently been obtained by Najati ...of additive and quadratic functional equation by ... See full document

... and after taking the limit in the resulting inequality, we see that Q satisfies (.). Using a similar method to the proof of Theorem . we see that Q is the unique quadratic mapping satisfying (.). Now letting ... See full document

... a quadratic functional ...the quadratic functional equation is said to be a quadratic ...the quadratic functional equation was proved by Skof 6 for mappings ... See full document

... the additive-quadratic-cubic functional ...Section 3, we prove the generalized Hyers-Ulam stability of the additive-quadratic- cubic functional ... See full document

... Keywords: Additive functional equations, Quadratic functional equations, Quartic functional equations, Mixed type functional equations, Ulam - Hyers stability, Ulam - Hyers - Rassias sta[r] ... See full document

... the quadratic functional equa- tion was proved by Skof [] for mappings f : X → Y , where X is a normed space and Y is a Banach ...the quadratic functional ... See full document

... Throughout this paper, let X be a normed linear space and Y a 2- Banach space. In 1941, D. H. Hyers [4] obtained the first result on the stability of the Cauchy functional equation. In 1950, T. Aoki [1] ... See full document

... the functional Equation ...ized quadratic functional equation and every solution of the generalized quadratic functional equation is said to be a generalized ... See full document

... Proof. Suppose that fx Ax Qx, x Cx, x, x for all x ∈ X, where A : X → Y is additive, Q : X × X → Y is symmetric and biadditive, and C : X × X × X → Y is symmetric and 3-additive. Then it is easy to ... See full document

... cubic functional equation, because the cubic function f (x) = cx 3 is a solution of the equation ...the functional equation ...X 3 → Y such that f (x) = C(x, x, x) for all ... See full document

... a functional equation arises when one replaces a func- tional equation by an inequality which acts as a perturbation of the ...approximate additive function and by Rassias [25] for approximate ... See full document

... We claim that the additive functional equation (1.14) is not stable for q = 1 in condition ( ii ) Corollary 3.1. Indeed, assume the contrary that there exist a additive mapping A : R n → R and ... See full document

... in which ⊥ is an orthogonality relation, is first investigated by Gudder and Strawther [13]. In 1985, Rätz [14] in- troduced a new definition of orthogonality by using more restrictive axioms than Gudder and Strawther. ... See full document

... type functional equations have been extensively investigated by a number of math- ematicians in referenes (see [3–5, 14–22, 28–31, 33–38, 43, 48, ... See full document

... the functional Equation ...several functional equations have been extensively investigated by a number of authors, and there are many inter- esting results concerning this problem (see ... See full document

... Jun, “On the generalized Hyers-Ulam-Rassias stability of an n-dimensional quadratic functional equation,” Journal of Mathematical Analysis and Applications, vol.. Park, “On the generaliz[r] ... See full document

... [19] Rassias, J.M. and Kim, H.M. (2009) Generalized Hyers-Ulam Stability for General Additive Functional Equation in Quasi- β -Normed Space. Journal of Mathematical Analysis and Applications , 356, ... See full document

... an additive mapping near an approximately additive mapping between a group and a metric group ...various functional equations have been extensively investigated by a number of authors [1-3,6,9- ... See full document

... Theorem 3.5. Let E be a normed vector space, F a Banach space and f : E → F a mapping which satisfies the inequality (3.10) for some θ ≥ 0, p > 2 and for all x, y ∈ E. Then there exists a unique mapping q : E → F , ... See full document