[PDF] Top 20 On the stability of a cubic functional equation in random 2 normed spaces

... Banach spaces and then generalized by Aoki [3] and Rassias [4] for additive mappings and linear mappings, ...several stability problems for various functional equations have been investigated in ... 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 ... See full document

... the cubic functional equations, since the function f(x) = cx 3 is their solu- ...the cubic functional equations is said to be a cubic ...The stability problem for the ... See full document

... Intmodellingtappliedtproblemstonlytpartialtinformationtmaytbet knownt(or)ttheretmaytbetatdegreetoftuncertaintytintthetparame terstusedtintthetmodeltortsometmeasurementstmaytbetimpreci se[r] ... See full document

... the stability of the linear mapping in Banach ...TM: Functional Equations, Inequalities and ...-fuzzy normed spaces and stability of functional ... See full document

... the stability of the linear functional ...the stability of the linear transformation in Banach ...Jpn. 2, 64-66 (1950) 22. Rassias, TM: On the stability of the linear mapping in Banach ... 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 ... See full document

... Ulam-Hyers stability problem for these cubic ...the functional equation 1.2, which is called a cubic functional equation and every solution of the cubic ... See full document

... the cubic functional equation since f (x) = cx 3 is its ...the cubic functional equation is said to be a cubic ...The stability problem of cubic ... See full document

... the cubic functional equation is said to be a cubic ...The stability problem for the cubic functional equation was solved by Jun and Kim 2 and Lee 3 for ... See full document

... : 2) It is easy to show that the function f(x) = x 3 satisfies the functional equation ...a cubic functional equation and every solution of the cubic functional ... See full document

... a cubic functional equation. Every solution of the cubic functional equation is said to be a cubic ...vector spaces X and Y is a solution of ... 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

... for all u v w , , ∈ U . Suppose an odd function g U : → V be a function with g (0) = 0 satisfies the inequality N Dg u v w ( ( , , ), ) y ≤ α ( , , ) u v w (3.1.34) for all u v w , , ∈ U and all y ∈ U . Then there exists ... See full document

... the stability of the linear functional ...the stability of the linear transformation in Banach ...Jpn. 2, 64-66 (1950) 37. Rassias, TM: On the stability of the linear mapping in Banach ... See full document

... In the sequel we adopt the usual terminology, notations and conventions of the theory of random normed spaces, as in 37–41. Throughout this paper, Δ is the space of all probability distribution ... 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

... The theory of fuzzy sets was introduced by Zadeh in 1965 [31]. After the pioneer- ing work of Zadeh, there has been a great effort to obtain fuzzy analogues of classical theories. Among other fields, a progressive ... 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 ... See full document

... fuzzy normed spaces to fuzzy β -normed spaces and adopt the fixed point and direct methods to prove the Hyers-Ulam-Rassias stability of the quartic functional equation f ... See full document