[PDF] Top 20 On the stability of a functional equation deriving from additive and quadratic functions

... a quadratic mapping. Skof [] solved the Hyers-Ulam stability problem of the quadratic functional equation in Banach ...the stability of the Euler-Lagrange quadratic ... See full document

... an additive function A such that f (x) = B(x, x) + ...type quadratic and additive func- tional ...investigated stability of ...the stability of the following functional ... See full document

... The functional equation 1.1 was first solved by Kannappan 15. In fact, he proved that a function on a real vector space is a solution of 1.1 if and only if there exist a symmetric biadditive function B and ... See full document

... an additive function A such that f (x) = B(x, x) + ...Hyers-Ulam stability of ...the stability of the following functional equation, which is a generalization of ... See full document

... The first stability problem was raised by S.M. Ulam [35] during his talk at the University of Wisconsin in 1940. In fact we are given a group ( G 1 , ·) and let ( G 2 , ∗) be a metric group with the metric d (· , ... See full document

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

... was proposed by Nakmahachalasint [14], where n is a positive integer with n > 1. He proved that (1.2) is equivalent to (1.1). For that reason, we say that (1.2) is a generali- zation of the Cauchy functional ... 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 ... 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

... Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4. In ... See full document

... f (2x + y) + f (2x − y) = 2f (x + y) + 2f (x − y) + 12f (x) (1:3) and they established the general solution and the generalized Hyers-Ulam stability for the functional equation (1.3). They proved ... See full document

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

... On quadratic set-valued ...s functional equation for set-valued ...of additive selection for ( α, β )-( β, α ) type subadditive set-valued ... 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 that ... 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

... distribution functions that is, the space of all mappings F : R ∪ {−∞, ∞} → 0, 1, such that F is left-continuous, non-decreasing on R, F0 0 and F∞ ...all functions F ∈ Δ for which l − F∞ 1, where l − fx ... 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

... in which ⊥ is an abstract orthogonality relation, was first investigated by Gudder and Strawther [3]. They defined ⊥ by a system consisting of five axioms and described the general semi-continuous real-valued solution of ... 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 ... See full document

... Hyers-Ulam Stability for General Additive Functional Equation in Quasi- β -Normed ...Hyers-Ulam Stability of a Functional Equation ... See full document