[PDF] Top 20 Stability of Additive-Quadratic Functional Equation in Banach Space and Banach Algebra: Using Direct and Fixed Point Methods

... The articles of Rassias[17,18] have provided a lot of influence in the development of what we now call generalized Ulam-Hyers[9,10,24] stability of functional equations. The terminology generalized Ulam- ... See full document

... Hyers-Ulam stability theorem for the quadratic functional equation ...normed space and E 2 be a Banach space, the result of Skof is still true if the relevant domain ... See full document

... The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [3, 7, 8, 9, 10, 30, 20, ... See full document

... the functional equation ...Hyers stability of the additive functional equation ...(1.8) using direct and fixed point methods are respectively ... 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 ... See full document

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

... of stability problem for functional equations goes back to a question raised by Ulam [44] concerning the stability of group homomorphisms that affirmatively answered for Banach spaces by Hyers ... See full document

... Throughout this paper, assume that (X ,P) is a Fr´echet space and (Y, || · ||) is a Banach space. One can easily show that an odd mapping f : X → Y satisfies (11) if and only if the odd mapping f : X ... 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

... a quadratic functional ...tic functional equation is said to be a quadratic ...Hyers-Ulam stability of the quadratic functional equation was proved by Skof ... 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 ... See full document

... a quadratic functional ...a quadratic mapping. A Hyers-Ulam stability pro- blem for the quadratic functional equation was proved by Skof [5] for mappings f : X → Y , where ... See full document

... such equation is called a quadratic functional ...the quadratic Equation ...is quadratic if and only if there exists a unique symmetric biadditive function B such that f (x) = B ... See full document

... for all t > 0. Therefore, A(x) = L(x) for all x Î X, this completes the proof. □ Corollary 2.6. Let X be a normed spaces and (ℝ, N’) a fuzzy Banach space. Assume that there exist real numbers θ ≥ 0 and 0 ... 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 the ... 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

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

... multi-normed space is introduced by Dales and Polyakov ...sequence space and has some connections with operator spaces and Banach ...the stability problems in mul- ti-Banach spaces are ... See full document

... In Ulam [1], the following question concerning the stability of homomorphisms is studied: Let G be a group and let H be a metric group with metric d(., .). Given ε > 0, there exists a δ > 0 such that if the ... 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 ... See full document