[PDF] Top 20 A fixed point approach to the stability of an additive cubic functional equation in paranormed spaces

... Hyers stability by replacing the bound θ (||x|| p ||y|| q ) in [9], by a mixed one involving the product and sum of powers of norms, that is, θ {||x|| p ||y|| p + (||x|| 2p + ||y|| 2p ... See full document

... a cubic functional equation, because the cubic function f (x) = cx 3 is a solution of the equation ...Hyers-Ulam-Rassias stability for the functional equation ... See full document

... of functional equations is as follows: when is it true that a function, which approximately satisfies a functional equation, must be close to an exact solution of the equation? If the problem ... 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

... 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

... The stability problem of functional equations is originated from a question of Ulam 1 concerning the stability of group ...Banach spaces. Hyers’ Theorem was generalized by Aoki 3 for ... See full document

... The stability problem of functional equations originated from the following question of Ulam [12]: Under what condition does there exist an additive mapping near an approximately additive ... See full document

... the stability of the additive mapping as a special ...Hyers-Ulam stability for the linear mapping between Banach spaces was ...Hyers-Ulam stability of the additive mapping was ... See full document

... a cubic functional equation. Every solution of the cubic functional equation is said to be a cubic ...vector spaces X and Y is a solution of ...each fixed ... See full document

... The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group ...Banach spaces. Hyers’s theorem was generalized by Aoki 3 for ... 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

... The stability problem of functional equations is originated from a question of Ulam 1 concerning the stability of group ...Banach spaces. Hyers’ Theorem was generalized by Aoki 3 for ... 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

... This stability phenomenon is called generalized Hyers-Ulam stability and has been extensively investigated for different functional ...the additive function C : E ® F is explicitly ... See full document

... The functional equation f(x + y) + f(x - y) = 2f(x) + 2f(y) is called a quadratic func- tional ...quadratic functional equation is said to be a quadratic ...Hyers-Ulam stability problem ... See full document

... The stability problem of functional equations originated from the question of Ulam [] concerning the stability of group ...Banach spaces. Hyers’ theorem was general- ized by Aoki [] for ... See full document

... of stability for functional equation arises when we replace the functional equation by an inequality which acts as a perturbation of the ...Banach spaces. Let f : X → X be a ... See full document

... Banach spaces. Hyers’ theorem was generalized by Aoki [] for additive mappings and by Rassias [] for linear mappings by considering an unbounded Cauchy ... See full document

... related stability results on ( β , p ) -Banach spaces, we refer to [19] ...-Banach spaces and extend previous result for quadratic functional ... See full document

... concerning stability of group homo- morphisms: Under what condition does there exist an additive mapping near an approximately additive mapping? Hyers [2] answered the problem of Ulam for Banach ... See full document