[PDF] Top 20 Orthogonal stability of mixed type additive and cubic functional equations

... f(x + y) = f (x) + f (y), (x, y ∈ A, x⊥y) (1.1) in which ⊥ is an abstract orthogonally was first investigated by S. Gudder and D. Strawther [7]. R. Ger and J. Sikkorska discussed the orthogonal stability of ... 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

... a cubic functional equation. Every solution of the cubic functional equation is said to be a cubic ...is additive for fixed two ... See full document

... quadratic, cubic and quartic functional equations and its Hyers-Ulam-Rassias stability were discussed by various authors ([3], [7], [12], [21], [24], [27], [29], [32], [34], ...the ... See full document

... quartic functional equation see also ...Hyers-Ulam stability for a mixed type of quartic and quadratic functional equation between two real linear Banach ...Hyers-Ulam stability ... See full document

... The stability of mixed 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

... concerning mixed functional equations have recently been obtained by Najati ...fuzzy stability of a mixed type of additive and quadratic functional equation by Park ... See full document

... a mixed type of quadratic and additive functional ...Hyers-Ulam-Rassias stability for a mixed type of cubic, quadratic and additive functional ... See full document

... Hyers-Ulam stability for general additive functional equations in quasi- β-normed spaces , ...the stability properties of a mixed type additive, quadratic and ... See full document

... Hyers-Ulam stability of different functional equations in random normed spaces, fuzzy normed spaces, and non-Archimedean fuzzy normed spaces has been recently studied in ... See full document

... the additive, the quadratic, the cubic, the quadratic-additive, the cubic- additive, the cubic-quadratic, and the cubic-quadratic-additive type ... See full document

... the stability of the linear functional ...the stability of the linear mapping in Banach ...S: Functional Equations and Inequalities in Several ...Hyers-Ulam-Rassias stability of ... See full document

... first stability problem concerning group ...for additive mappings. For additive mapping involving dif- ferent powers of norms ...This stability is also investigates by Park ...other ... See full document

... Jun and Kim proved that a function f between real vector spaces X and Y is a solution of 1.5 if and only if there exists a unique function C : X × X × X → Y such that fx Cx, x, x for all x ∈ X, and C is symmetric for ... See full document

... the functional equation (1.5). Inter- esting new results concerning mixed functional equations has recently been obtained by Najati ...fuzzy stability of a mixed type of ... See full document

... of stability theory of functional equations for the proof of new fixed point theorems with ...The stability problems of several various functional equations have been extensively ... See full document

... equation. Every solution of the cubic functional equation is said to be a cubic mapping. Jun and Kim proved that a mapping f between two real vector spaces X and Y is a solution of 1.1 if and only if ... See full document

... From now on, unless otherwise stated, we will assume that X is a non-Archimedean normed space and Y is a non-Archimedean Banach space. Utilizing the fixed point alternative, we investigate the Hyers-Ulam stability ... See full document

... When the Hyers’ theorem is true even if we replace ε and K(ε) by ϕ(x) and Φ(x), where ϕ and Φ are functions not depending on f and F explicitly, the corresponding equation is said to have (or satisfy) the generalized ... See full document

... Theorem 2.4. Let (X, · ) with dimX ≥ 2 be a real normed linear space with Birkhoff- James orthogonality and let (Y , · ) be a real Banach space. If a function f : X → Y satisfies (2.1) for some ε ≥ 0, p ∈ R \ { 1, 2 } , ... See full document