[PDF] Top 20 On nonlinear stability in various random normed spaces

... Theorem 4.2. Let K be a non-Archimedean field, X a vector space over K and let (Y, μ, T)be a non-Archimedean random Banach space over K . Let f : X → Ybe a Ψ- approximately quartic mapping. If for some a Î ℝ, a ... 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

... the stability of the linear transformation in Banach spaces, ...Fuzzy Stability of n-Dimensional Quadratic Functional Equation: Direct and Fixed Point Methods, ... See full document

... The stability problem for the quadratic functional equation first was proved by ...real normed space and Y is a Banach ...the stability in the settings of fuzzy, probabilistic, and random ... See full document

... answer to the question of Ulam for Banach spaces. Hyers’ theorem was generalized by Aoki 5 for additive mappings and by Th. M. Rassias 6 for linear mappings by considering an unbounded Cauchy difference. The paper ... 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

... on stability of equation g ax a s gx a, s ∈ N, a ≥ 2 in random normed spaces and derive from it results on stability of equation f4x 10f2x − ...Ulam-Hyers stability for the ... 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 ...Banach spaces. Let f : E → E be a mapping between Banach ... See full document

... Ulam-Hyers stability results for functional equations defined by mappings with values in probabilistic metric spaces and in random normed spaces, obtained by using the fixed point ... See full document

... is thus called a cubic functional equation. Every solution of the cubic functional equation is said to be a cubic function. Also, Jun and Kim proved that a function f between real vector spaces X and Y is a ... 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

... 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 types ... 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

... f (x+3y)3 f (x + y)+3 f (xy) f (x3y) =48 f (y) (1.1) is said to be the cubic functional equation since f (x) = cx 3 is its solution. Every solution of the cubic functional equation is said to be a cubic mapping. The ... See full document

... the stability in random normed spaces and in non-Archimedean spaces, moreover, the stability for functions from quasi-normed spaces into p–Banach spaces and ... See full document

... HU Stability is consequence of study of Ulam’s [1] problem regarding stability of group ...HU Stability under various ...HU stability in Banach spaces and non- Archimedean Banach ... 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

... mentioned stability involving a product of powers of norms is called Ulam- Gavruta-Rassias stability by various authors see ...Ulam-Hyers stability are dealt with in various ... See full document

... of stability theory of functional equations for the proof of new fixed point theorems with ...The stability problems of several various functional equations have been extensively investigated by a ... 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 answer to the ... See full document