[PDF] Top 20 On the stability of a mixed type quadratic additive functional equation

... 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

... 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

... 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 answered ... See full document

... Hyers-Ulam stability of different functional equations in random normed spaces, RN- spaces and fuzzy normed spaces has been recently studied in, Alsina 44, Mirmostafaee, Mirzavaziri and Moslehian 33, 45–47, ... See full document

... this equation is called a quadratic functional ...the quadratic functional equation ...is quadratic if and only if there exists a unique symmetric bi-additive ... 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

... 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

... Hyers-Ulam stability of the Cauchy additive functional equa- tion, the quadratic functional equation ...cubic functional equation (.) and the quartic ... 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 equa- tions have been extensively ... 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

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

... an additive functional equations. Also, we obtain its general solution from the stability results. Copyright q 2008 Kil-Woung Jun et al. This is an open access article distributed under the Creative ... 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 quadratic functional ...the quadratic functional equation is said to be quadratic ...of stability theory of functional equations for the proof of new fixed ... 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

... It is to be noted that, Mirmostafaee and Moslehian [28] initiate a notion of a non-Archimedean fuzzy norm and studied the stability of the Cauchy equation in the context of non-Archimedean fuzzy spaces. ... 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 cubic ... See full document

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

... f (2x + y) + f (2x − y) = 4[ f (x + y) + f (x − y)] + 24 f (x) − 6 f (y) (1.5) and discussed its general solution. In fact Lee et al. [17] proved that a function f between vector spaces X and Y is a solution of (1.5) if ... See full document