[PDF] Top 20 Stability of a Quadratic Functional Equation in the Spaces of Generalized Functions

... unknown functions, which is not required in direct ...with functional equations based on distribution ...some functional equations in distributions reduce to the classical ones when the solutions are ... See full document

... the equation for the spaces of generalized ...heat equation we solve the general solutions and the stability problems of this equation in the spaces of tempered ... See full document

... the stability problems of (.) in the spaces of generalized functions such as S of tempered distributions, F of Fourier hyper- functions and D of ...the spaces of ... See full document

... Therefore, from (5.6), we conclude that Q = Q 0 . This completes the proof. Corollary 5.3. Let K be a non-Archimedean field, X a vector space over K and (Y, P , T ) a non-Archimedean L-fuzzy Banach space over K under a ... 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

... If p < 0 or q < 0, the right-hand side of (1.7) does not define a distribution and so inequality (1.7) makes no sense. If p,q = 3, it is not guaranteed whether Hyers-Ulam- Rassias stability of (1.5) is hold ... See full document

... The generalized Hyers-Ulam stability problem for the quadratic functional equation ...the generalized Hyers-Ulam stability of the functional equation ...has ... See full document

... The stability problem of functional equations originated from the following question of Ulam[19]: Under what condition does there exist an additive mapping near an approximately additive mapping? In 1941, ... See full document

... a quadratic functional equation. Quadratic functional equations were used to characterize inner product ...the quadratic equation is said to be a quadratic ...The ... See full document

... a quadratic functional equation. Quadratic functional equations were used to characterize inner product spaces ...the quadratic equation ...vector spaces is ... 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

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

... a quadratic functional ...the quadratic equation ...vector spaces is quadratic if and only if there exists a unique symmetric bi-additive function B 1 such that f (x) = B 1 (x, ... See full document

... Our results are organized as follows: In section 2, we determine the general solution of the functional equation (1.5). In section 3, we prove the Hyers-Ulam-Rassias sta- bility of the equation (1.5) ... See full document

... quasi-Banach spaces, where k is nonzero integer numbers with k ≠ ± ...the functional equation ...mixed functional equations has recently been obtained by Najati ...fuzzy stability of a ... See full document

... the generalized Hyers-Ulam stability of functional equa- tion (b) and functional inequality (c) has been presented in ...the stability of functional inequalities and the ... See full document

... The functional equation f (x + y) = f (x) + f(y) is called the Cauchy ...Cauchy equation is said to be an additive ...Banach spaces. Hyers’ Theorem was generalized by Aoki [1] for ... See full document

... The functional equation f (x + y) = f (x) + f(y) is called the Cauchy ...Cauchy equation is said to be an additive ...Banach spaces. Hyers’ Theorem was generalized by Aoki [2] for ... See full document

... the stability problem of functional equations which was first raised by ...Banach spaces. A generalized version of the theorem of Hyers for approximately linear mappings was given by ... See full document

... normed spaces, as in ...distribution functions that is, the space of all mappings F : R ∪ {−∞, ∞} → 0, 1, such that F is leftcontinuous and nondecreasing on R, F0 0 and F∞ ...all functions F ∈ Δ for ... See full document