[PDF] Top 20 Stability of functional inequalities in matrix random normed spaces

... is called the Cauchy additive functional equation. In particular, every solution of the Cauchy additive functional equation is said to be an additive mapping. Hyers [] gave the first affirmative partial ... See full document

... Katsaras [] 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 [–]. In ... See full document

... HU Stability is consequence of study of Ulam’s [1] problem regarding stability of group ...HU Stability under various ...-functional inequalities and proved their HU stability in ... See full document

... Let X is a linear space of a dimension d, where 2 ≤ d < ∞ . A 2-normed on X is a function ∥ ., . ∥ : X × X ® ℝ satisfying the following conditions, for every x, y Î X (i) ∥ x, y ∥ = 0 if and only if x and y are ... See full document

... is called the Cauchy additive functional equation. In particular, every solution of the Cauchy additive functional equation is said to be an additive mapping. Hyers [] gave the first affirmative partial ... See full document

... for all x ∈ E. Moreover if ftx is continuous in t ∈ R for each fixed x ∈ E, then T is linear. In 1978, Rassias 3 provided a generalization of Hyers’ Theorem which allows the Cauchy difference to be unbounded. In 1991, ... See full document

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

... This phenomenon is called generalized Ulam-Hyers stability and has been extensively investigated for different functional equations. Almost all proofs used the idea conceived by Hyers. Namely, the additive ... See full document

... 47. Agarwal, RP, Cho, YJ, Saadati, R: On random topological structures. Abstr Appl Anal, Art ID (2011). 762361, 41 48. Krishna, SV, Sarma, KKM: Separation of fuzzy normed linear spaces. Fuzzy Sets ... See full document

... In the sequel, we adopt the usual terminology, notations, and conventions of the theory of random normed spaces as in [–]. Throughout this paper, + is the space of dis- tribution functions, that ... See full document

... Conversely, let fx Cx, x, x Qx, x for all x ∈ X, where the function C is symmetric for each fixed one variable and is additive for fixed two variables and Q is biadditive. By a simple computation, one can show that the ... See full document

... additive functional equation for n ≥ 2 and then investigate the stability in random normed spaces and in non-Archimedean spaces, moreover, the stability for functions from ... 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

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

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

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

... of stability for func- tional equation arises when we replace the functional equation by an inequality which acts as a perturbation of the ...Banach spaces. Let f : E ® E’ be a mapping between Banach ... See full document

... probabilistic normed spaces briefly, PN-spaces is important as a generalization of deterministic result of linear normed spaces and also in the study of random operator ... See full document

... cubic functional equation is said to be a cubic mapping. 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 ... See full document

... a normed space and Y is a Banach ...The stability problem of several functional equations have been investigated by a number of authors and there are many interesting results concerning this problem ... See full document