[PDF] Top 20 Fuzzy Stability of Additive Functional Inequalities with the Fixed Point Alternative

... of fuzzy normed spaces given in 5, 9, 10 to investigate a fuzzy version of the generalized Hyers-Ulam stability for the Cauchy additive functional inequality and for the Cauchy-Jensen ... See full document

... the stability of functional equation was first suggested by Hyers 17 while he was trying to answer the question originated from the problem of Ulam 18, and it is called a direct method because it allows us ... See full document

... given functional equation and is seen to be a powerful tool for studying the stability of many functional ...several stability problems and its fuzzy version for var- ious ... See full document

... to point out the direct method for studying the stability of func- tional ...the fixed point alternative method to solve the Ulam ...the fixed point alternative ... See full document

... the stability of the linear functional ...the stability of the linear transformation in Banach ...the stability of the linear mapping in Banach ...Hyers-Ulam-Rassias stability of ... See full document

... The stability problem of functional equations originated from the following question of Ulam [18]: Under what condition does there exist an additive mapping near an approximately additive ... See full document

... in which ⊥ is an abstract orthogonality relation, was first investigated by Gudder and Strawther []. They defined ⊥ by a system consisting of five axioms and described the gen- eral semi-continuous real-valued solution of ... See full document

... of stability for a functional equation arises when we re- place the functional equation by an inequality which acts as a perturbation of the ...for additive mappings and by Rassias [] for ... See full document

... 13. Nikodem, K: On quadratic set-valued functions. Publ Math Debrecen. 30, 297 – 301 (1984) 14. Nikodem, K: On Jensen ’ s functional equation for set-valued functions. Radovi Mat. 3, 23 – 33 (1987) 15. Nikodem, K: ... See full document

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

... orthogonal stability of the Cauchy functional equation f(x + y) = f(x) + f(y), namely, they showed that if f is a mapping from an orthogonality space X into a real Banach space Y and ∥f(x + y) - f(x) - ... See full document

... a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the ...defined fuzzy norms on a vector space from various points of view ...of fuzzy norm in such a manner ... See full document

... Theorem 3.5 (Fixed point alternative). Let (X, d) be a complete generalized metric space and a contractive mapping J: XX, with the Lipschitz constant L. Then, for each given element xX, either (A 1 ... See full document

... The rest of the proof is similar to the proof of Theorem .. Corollary . Let θ ≥  and let p be a real number with  < p < . Let X be a normed vector space with the norm · . Let f : X → Y be an odd mapping ... See full document

... functional equations. The paper of Rassias 4 had great influence on the development of a generalization of the Hyers-Ulam stability concept. This new concept is known as Hyers-Ulam- Rassias stability ... See full document

... the functional equation ...Hyers stability of the additive functional equation ...and fixed point methods are respectively ...the additive functional equation ... See full document

... equality fx y − fx − f y ≤ ε, for all x and y, can be approximated by an exact so- lution, say an additive function. Later, the result of Hyers was significantly generalized for additive mappings by Aoki 3 ... See full document

... 15 proved the Hyers-Ulam stability of quadratic functional 1.1 by the similar way to Th. M. Rassias control function 5. According to the theorem of Borelli and Forti 16, we obtain the following ... See full document

... quintic functional equation f x 3y − 5fx 2y 10fx y − 10fx 5fx − y − fx − 2y 120fy and the sextic functional equation fx 3y − 6fx 2y 15f x y − 20f x 15f x − y − 6f x − 2y f x − 3y 720f y ...the ... See full document

... of stability theory of functional equations for the proof of new fixed point theorems with applica- ...using fixed point methods, the stability problems of several ... See full document