[PDF] Top 20 On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi Banach Spaces

... the functional equation ...the functional equation 1.6 when f is a mapping between vector spaces, and we establish the generalized Hyers-Ulam stability of this ... 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 view 2–4. In ... See full document

... this equation is called a quadratic functional ...the quadratic equation ...vector spaces is quadratic if and only if there exits a unique symmetric bi-additive mapping B ... See full document

... operator spaces and Banach ...multi-normed spaces and many examples are given in [17]. Also, the stability problems in mul- ti-Banach spaces are studied by Dales and Moslehian ... See full document

... normed spaces RN-spaces is important as a generalization of deterministic result of linear normed spaces and also in the study of random operator ...The generalized Hyers-Ulam stability ... See full document

... the generalized Hyers-Ulam-Rassias sta- bility for a mixed type of quadratic and additive functional ...Hyers-Ulam-Rassias stability for a mixed type of cubic, quadratic ... See full document

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

... Cauchy functional equation gxy gxgy respectively, the Jensen functional equation 2gxy/2 ...Hyers-Ulam stability by considering variables for Cauchy ...Jensen equation. It also ... See full document

... on Functional Equations asked the question whether such a theorem can also be proved for p ≥ ...Rassias’ type theorem when p = ...similar stability theorem in which he replaced the unbounded Cauchy ... See full document

... 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 ... See full document

... of quadratic, cubic and quartic functional equations and its Hyers-Ulam-Rassias stability were discussed by various authors ([3], [7], [12], [21], [24], [27], [29], [32], [34], ...mixed ... See full document

... the stability of the Cauchy functional ...the generalized Hyers-Ulam stability ...the generalized Hyers- Ulam stability of the equation ... See full document

... first stability problem concerning group ...in Banach spaces. Aoki [14] generalized Hyers result for additive ...This stability is also investigates by Park ...other type fuzzy ... See full document

... We introduce a basic property of a quasi-(2;p)-normed space as follows. Let (X , k·, ·k) be linear quasi-(2;p)-normed space, x ∈ X and k x, y k= 0 for each y ∈ X. suppose x 6= 0. Since dim X > 1, choose ... See full document

... in Banach spaces, which is also a quadratic and equivalent to ...and generalized Hyers-Ulam stability of ...the functional equation ...and equation (0.2) in complex ... 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

... the functional equation ...of functional equation 1.7 when f is a function between vector spaces, and then we prove the generalized Hyers-Ulam stability of ... See full document

... of stability for functional equation arises when we replace the functional equation by an inequality which acts as a perturbation of the ...for Banach spaces. Let f : E → ... 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 ... See full document

... the stability problem of functional equations originated from the question of Ulam [, ] concerning the stability of group ...Banach spaces. Later, Aoki [] and Bourgin [] considered ... See full document