[PDF] Top 20 Functional Equation and Its Hyers Ulam Stability

... proof of Theorem 2.1 can be derived from theorems presented in the books 19, 20. However, the theorems in 19, 20 deal with solutions of the linear equation under some regularity conditions, for example, the ... See full document

... Taking this fact into account, the additive Cauchy functional equation f (x + y) = f (x) + f (y) is said to have the Hyers-Ulam stability. This terminology is also applied to the case ... See full document

... a Hyers-Ulam stability problem for the quadratic functional equation was proved by Skof [5] for mappings f : X ® Y, where X is a normed space and Y is a Banach ...the Hyers- ... See full document

... functional equation. In particular, every solution of the quadratic functional equation is said to be a quadratic ...A Hyers-Ulam stability problem for the quadratic ... See full document

... Rassias, “On the ulam stability of Jensen and Jensen type mappings on restricted domains,” Journal of Mathematical Analysis and Applications, vol.. Park, “On the solution of a bi-Jensen [r] ... See full document

... The stability problem of functional equations originated from a question of Ulam [] concerning the stability of group ...homomorphisms. Hyers [] gave the first affirmative partial ... See full document

... resulting equation by θ n (resp.γ n ) and replace n by −m in the resulting equation, then we obtain a equation with m in place of n, where m ∈ {0, −1, −2, ... See full document

... S.M. Ulam [47] introduced the stability of functional ...H. Hyers [16] gave first confirmatory answer to the Ulam question for Banach ...1978, Hyers theorem was generalized by ... See full document

... the Hyers theorem (Hyers-Ulam-Rassias stability ...terminologies Hyers-Ulam stability and Hyers-Ulam-Rassias stability can also be applied to the case ... See full document

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

... the functional equation (1.5). In section 3, we prove the Hyers-Ulam-Rassias sta- bility of the equation ...the Hyers-Ulam stability of equation ... See full document

... H. Hyers [6] for the first ...the stability problem of functional equations has been extended in various directions and studied by several mathematicians (see [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...the ... See full document

... generalized Hyers-Ulam stability problem for the quadratic functional equa- tion was proved by Skof [] for mappings f : X → Y , where X is a normed space and Y is a Banach ...generalized ... See full document

... the Hyers-Ulam stability of Cauchy additive functional inequality ...the Hyers-Ulam stability of the Cauchy additive functional equation in matrix paranormed ... See full document

... by Hyers [4], when G and G 0 are Banach space. Since then, the stability problems of functional equations have been extensively investigated by several math- ematicians ...the ... See full document

... G˘avrut¸a [10] provided a further generalization of Rassias’ theorem. During the last two decades, a number of papers and research monographs have been published on vari- ous generalizations and applications of the ... See full document

... functional equation. In particular, every solution of the quadratic functional equation is said to be a quadratic ...A Hyers-Ulam stability problem for the quadratic ... See full document

... called Hyers-Ulam-Rassias stability or generalized Hyers-Ulam stability of functional ...the stability of the equation of homomorphism, ... See full document

... The Hyers-Ulam- Rassias stability of the quartic functional equation ...the stability of the quartic functional equation ... See full document

... generalized Hyers-Ulam-Rassias stability of functional ...D.H. Hyers was proved by ...of stability of functional equations involving with the mixed type product-sum of ... See full document