[PDF] Top 20 On the Stability of Generalized Quartic Mappings in Quasi Normed Spaces

... For this reason, 1.1 is called a quartic functional equation. Also Chung and Sahoo 12 determined the general solution of 1.1 without assuming any regularity conditions on the unknown function. In fact, they proved ... See full document

... For this reason, 1.1 is called a quartic functional equation. Also Chung and Sahoo 16 determined the general solution of 1.1 without assuming any regularity conditions on the unknown function. In fact, they proved ... See full document

... a quasi- β -Banach space is called a ( β , p ) -Banach ...of quasi-normed spaces and p-Banach ...each quasi-norm is equal to some ...then quasi-norms, we restrict our attention ... See full document

... of stability problems of functional equations, the stability phenomenon that was proved by Rassias may be called the Hyers-Ulam-Rassias stability see 5, ... See full document

... a quartic functional equation see also ...the generalized Hyers-Ulam stability for a mixed type of quartic and quadratic functional equation between two real linear Banach ...the ... See full document

... the stability of quartic mapping in fuzzy normed ...that quartic mapping exist another fuzzy approximately quartic ...the quartic mapping be a fuzzy continuity ... See full document

... the stability of the cubic functional equation f2x y f2x − y 2fx y 2fx − y 12fx in fuzzy normed spaces was proved in earlier work; and the stability of the additive functional equations fx y ... See full document

... 4(f (3x + y) + f(3x − y)) = −12(f(x + y) + f (x − y)) + 12(f(2x + y) + f (2x − y)) − 8f (y) − 192f (x) + f (2y) + 30f (2x). (1.5) It is easy to see that the function f : R → R defined by f(x) = ax 4 +bx 3 is a solution ... See full document

... of stability problems for functional equations is related to a question of Ulam [30] concerning the stability of group homomorphisms and affirmatively answered for Banach spaces by Hyers ...was ... See full document

... the stability problems of functional equations is as follows: when is it true that a mapping satisfying a functional equation approximately must be close to the solution of the given functional equation? Such an ... See full document

... In the sequel we adopt the usual terminology, notations, and conventions of the theory of random normed spaces, as in 19–21. Throughout this paper, Δ is the space of distribution functions that is, the ... See full document

... Hyers-Ulam-Rassias stability with the generalized control function. This stability result is called the Hyers-Ulam-Rassias stability of functional ...the quartic functional ... See full document

... multi-normed spaces, and investigate some properties of multi-bounded mappings on multi-normed ...a generalized Hyers–Ulam–Rassias stability theorem associated to the Cauchy ... See full document

... The stability problem for the cubic functional equation was solved by Jun and Kim 2 and Lee 3 for mappings f : X → Y , where X is a real normed space and Y is a Banach ...the stability of some ... 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 additive ... See full document

... The stability problem of functional equations originated from a question of Ulam 13 concerning the stability of group ...Banach spaces. Hyers’ theorem was generalized by Aoki 15 for additive ... See full document

... was generalized in various directions. The very first author who generalized Hyers’ theorem to the case of unbounded control functions was ...difference generalized Hyers’s Theorem for the ... See full document

... In 2000, Lee and Jun 14 have improved the stability problem for approximately additive mappings. The problem when p 1 is not true. Counter examples for the corresponding assertion in the case p 1 were ... See full document

... for all x, y, z ∈ X.k·, ·k is called a 2-normed and (X , k·, ·k) is called a linear 2-normed space. It is known that equality holds for every in definition (1.1) part (4) if and only if x and y are linearly ... See full document

... On Generalized Fuzzy Normed Spaces, International Mathematical Forum, 4, 2009, ...the stability of the linear functional equation, ...Rassias, Stability of functional equations in ... See full document