[PDF] Top 20 Fuzzy Stability of an Additive Quadratic Quartic Functional Equation

... The stability problem of functional equations originated from a question of Ulam 13 concerning the stability of group ...for additive mappings and by ...Hyers-Ulam stability or as ... See full document

... Hyers-Ulam stability problem for the quadratic functional equation was proved by Skof [5] for mappings f : X ® Y, where X is a normed space and Y is a Banach ...Hyers-Ulam stability of ... See full document

... a quadratic functional equation. Quadratic functional equations were used to characterize inner product ...the quadratic equation is said to be a quadratic ... See full document

... orthogonal stability of the Cauchy functional equation f(x + y) = f(x) + f(y), namely, they showed that if f is a mapping from an orthogonality space X into a real Banach space Y and ∥f(x + y) - f(x) ... See full document

... Jensen functional equation see 12, 13 for the first ...the stability problems of several functional equations have been extensively investigated by a number of ... See full document

... an equation is called a quadratic functional ...the quadratic equation ...is quadratic if and only if there exists a unique symmetric bi- additive function B such that f ... 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

... for additive mappings and by Ras- sias [] for linear mappings by considering an unbounded Cauchy ...Hyers-Ulam-Rassias stability of functional ... See full document

... of functional equations is the following: ‘When is it true that a function which approximately satisfies a functional equation must be close to an ex- act solution of the equation?’ If the ... See full document

... Proof. The proof follows from Theorem 2.3 by taking (x, y, z): = θ(||x|| p · ||y|| p · || z|| p ) for all x, y, z Î X. Then we can choose L = 2 -3p and we get the desired result. □ 2.2. Direct method. In this subsection, ... See full document

... be quadratic functional equation because the quadratic function f (x) = ax 2 is a solution of the functional equation ... See full document

... which is mixed of a quadratic and an additive functional equations. In this paper, we establish the generalized Hyers-Ulam-Rassias stability for 1.6 on the punctured domain V \ {0} and obtain ... See full document

... Generalized Fuzzy Normed Spaces, International Mathematical Forum, 4, 2009, ...the stability of the linear functional equation, ...Rassias, Stability of functional equations in ... See full document

... HU Stability is consequence of study of Ulam’s [1] problem regarding stability of group ...HU Stability under various adaptations. Park [16],[17] introduced additive ρ -functional ... See full document

... the functional equation ...the functional equation ...Hyers-Ulam stability of this functional equation whenever f is a mapping between two quasi-Banach ... 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

... since n−1 j0 1/22 p /4 j 2 p /2 j ≤ 24 − 2 p 2 − 2 p /4 − 2 p 2 − 2 p . Because 0 < ε < 1 is arbitrary, we get inequality 2.3 in this case. Finally, to prove the uniqueness of F, let F : X → Y be another ... See full document

... orthogonal stability of the Cauchy functional equation f(x + y) = f(x) + f(y), namely, they showed that if f is a mapping from an orthogonality space X into a real Banach space Y and ||f(x + y) - ... See full document

... unique additive mapping A : X → Y, a unique mapping C : X × X × X → Y , and a unique symmetric multi-additive mapping Q : X × X × X × X → Y such that fx Ax Cx, x, x Qx, x, x, x for all x ∈ X, and that C is ... See full document

... a quadratic functional ...the quadratic functional equation is said to be a quadratic ...Hyers-Ulam stability problem for the quadratic functional ... See full document