[PDF] Top 20 Stability of a Jensen type quadratic additive functional equation under the approximately conditions

... of stability problems for functional equations has originally been raised by Ulam []: under what condition does there exist a homomorphism near an approximate homomorphism? In , Hyers [] had ... See full document

... the functional equation ...mixed functional equations has recently been obtained by Najati ...fuzzy stability of a mixed type of additive and quadratic functional ... 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

... on Functional Equations asked the question whether such a theorem can also be proved for p ≥ ...Rassias’ type theorem when p = ...new approximately additive or approximately linear ... 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

... Hyers-Ulam stability problems of functional equations go back to 1940 when Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group (see ...[2,3] under the ... See full document

... that under some suitable conditions, an approximately mixed additive-quadratic function can be approximated by a mixed additive and quadratic ... See full document

... are said to be Jensen- Type Quadratic functional equations. In 2009, S.Y.Jang, Rye Lee, Choonkil Park, and Dong Yun Shin [24] proved the Fuzzy stability of equation (1.3) and ... See full document

... The notion of quasi-β-normed space was introduced by Rassias and Kim []. This no- tion is similar to quasi-normed space. We fix a real number β with  < β ≤  and let K = R or C . Let X be a linear space over K . A ... 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 ... See full document

... an approximately homomorphism between a group and a metric group? This is called the stability problem of functional equations which was first raised by ...Ulam under the assumption that the ... See full document

... If the problem accepts a solution, we say that the equation is stable. The first sta- bility problem concerning group homomorphisms was raised by Ulam [35] in 1940. In the next year, Hyres [11] gave a positive ... 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

... 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 conditions (A), (B) will be needed to derive a quadratic mapping, and one of the conditions (C), (D) will be required to derive an additive mapping in the following ... See full document

... fuzzy stability prob- lems for the Cauchy additive functional equation, the Jensen additive functional equation and the cubic functional equation in ... 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

... On quadratic set-valued ...On Jensen ’ s functional equation for set-valued ...of additive selection for ( α, β )-( β, α ) type subadditive set-valued ... See full document

... of stability problems of functional equations, the stability phenomenon that was proved by Rassias is called the gen- eralized Ulam-Rassias stability or Hyers-Ulam-Rassias stability ... See full document

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