[PDF] Top 20 A fixed point approach to the stability of a functional equation on quadratic forms

... A fixed-point approach to the stability of a functional equation on quadratic forms Jae-Hyeong Bae1 and Won-Gil Park2* * Correspondence: [email protected] 2 Department of Mathematics E[r] ... See full document

... of stability problems for functional equations is related to a question of Ulam [1] concerning the stability of group homomorphisms and affirmatively answered for Banach spaces by Hyers ... See full document

... Assume that inequality 3.3 is also satisfied with another function G : a, ∞ → C which is a solution of 1.1. As G is a solution of 1.1, G satisfies that Gx Gx 1 − i/ √ x 1Gx ΛGx for all x ≥ a. In other words, G is a ... See full document

... Hyers-Ulam-Rassias stability of C ∗ -algebra homomorphisms and of generalized derivations on C ∗ -algebras for the following Cauchy-Jensen functional equation 2fx y/2 z fx fy 2fz, which was ... 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 proved by Aoki see ... See full document

... of functional equations araised 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 ... See full document

... The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group ...Hyers-Ulam-Rassias stability of functional ... See full document

... in non-Archimedean normed spaces and in random normed spaces, where m , n are different integers greater than 1. In this article, using fixed point method, we prove the Hyers-Ulam stability of the ... See full document

... for all x, y ∈ E, controlled by a product of different powers of norms, where θ ≥ 0 and real numbers p, q, r : p q / 1, and retained the condition of continuity of f tx in t ∈ R for each fixed x ∈ E. Besides he ... See full document

... the fixed point method to prove the Hyers-Ulam-Rassias stability of the functional equation ...Hyers-Ulam-Rassias stability approach for the proof of new fixed ... See full document

... a quadratic functional ...the quadratic functional equation is said to be a quadratic ...Hyers-Ulam stability problem for the quadratic functional ... See full document

... of functional equations is as ...a functional equation must be close to an exact solution of the equation?” The first stability problem concerning group homomorphisms was raised by Ulam ... See full document

... The fixed point alternative methods are implemented to give generalized Hyers-Ulam-Rassias stability for the Pexiderized quadratic functional equation in the fuzzy ...the ... See full document

... the quadratic equation ...is quadratic if and only if there exists a unique symmetric biadditive mapping B such that f x Bx, x for all x see 16, 21, 26, ... See full document

... called quadratic functional ...of functional eqaution ...a quadratic mapping. A Hyers-Ulam stability problem for the quadratic functional equation was proved by ... See full document

... 4. Stability of the generalized quadratic set-valued functional Equation ...the fixed point method, we define a generalized quadratic set-valued functional ... See full document

... The stability problem of functional equations originated from the following question of Ulam [18]: Under what condition does there exist an additive mapping near an approximately additive mapping? In 1941, ... See full document

... the bound of Cauchy difference by a general control function. During the last two decades a number of papers and research monographs have been published on various generalizations and applications of the generalized ... 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

... These kinds of the questions from the basis of stability theory, and D.H.Hyers [14,15] obtained the first important result in this field .Many examples of this have been solved and many variations have been ... See full document