[PDF] Top 20 Solution and Stability of a Mixed Type Additive, Quadratic, and Cubic Functional Equation

... unique additive function A : X → Y , a unique symmetric and biadditive function Q : X × X → Y, and a unique symmetric and 3-additive function C : X × X × X → Y such that fx Ax Qx, x Cx, x, x for all x ∈ ... See full document

... a quadratic functional ...every solution of the quadratic functional equation is said to be a quadratic ...Hyers-Ulam stability problem for the quadratic ... 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

... equation: f(kx + ly) + f(kx – ly) = f (kx) + f (x) + 1 2 (k – 1)[(k + 2)f (x) + kf(–x)] + l 2 [f (y) + f(–y)] (k,l ∈ Z\{0}) in β -Banach modules on a Banach algebra. In addition, we show that under some suitable ... See full document

... the functional equation ...general solution of the functional equation ...Hyers-Ulam stability of this functional equation whenever f is a mapping between two ... See full document

... on stability of equation g ax a s gx a, s ∈ N, a ≥ 2 in random normed spaces and derive from it results on stability of equation f4x 10f2x − ...Ulam-Hyers stability for the general ... See full document

... In 1984, Katsaras 17 defined a fuzzy norm on a linear space to construct a fuzzy structure on the space. Since then, some mathematicians have introduced several types of fuzzy norm in different points of view. In ... 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

... Hyers-Ulam stability of the Cauchy additive functional equa- tion, the quadratic functional equation ...the cubic functional equation (.) and the quartic ... See full document

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

... on Functional Equations asked the question whether such a theorem can also be proved for p ≥ ...affirmative solution to this question for p > ...Rassias’ type theorem when p = ...approximately ... See full document

... The stability problem of functional equations is originated from a question of Ulam 1 concerning the stability of group ...for additive mappings and by ...Hyers-Ulam stability or as ... See full document

... The stability problem of functional equations originated from a question of ...the stability of group ...approximate additive mappings was given by ... See full document

... In fact, they proved that a mapping f between two real vector spaces X and Y is a solution of 1.2 if and only if there exists a unique symmetric multi-additive mapping B : X ×X ×X ×X → Y such that fx Bx, x, ... See full document

... The notion of multi-normed space is introduced by Dales and Polyakov [17]. This concept is somewhat simi- lar to operator sequence space and has some connections with operator spaces and Banach lattices. Motivations for ... See full document

... a quadratic functional equation because the quadratic function f (x) = ax 2 is a solu- tion of the functional equation ...A quadratic functional equation was ... See full document

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

... of 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

... Under what condition is there a homomorphism near an approximately homomorphism between a group and a metric group? This is called the stability problem of functional equations which was first raised by S. ... See full document

... general solution and the generalized Hyers-Ulam stability for the functional equation ...a solution of ...is additive for fixed two ... See full document