[PDF] Top 20 A general uniqueness theorem concerning the stability of monomial functional equations in fuzzy spaces

... Hyers-Ulam stability problems of monomial functional equations, we have been frequently requested to prove the uniqueness of the monomial mappings un- der various ...references ... See full document

... probabilistic stability of the monomial functional ...On stability of the general linear ...A general uniqueness theorem concerning the stability of ... See full document

... The stability problem of functional equations originated from a question of Ulam [] concerning the stability of group ...Banach spaces. Hyers’ theorem was generalized by ... See full document

... induced fuzzy metric is of the Kramosil and Michálek type ...decomposition theorem of a fuzzy norm into a family to crisp norms and gave some properties of fuzzy ...The fuzzy ... See full document

... ’ theorem for additive mappings, and in 1978, ...The stability problems of several functional equations have been extensively investi- gated by a number of authors, and there are many ... See full document

... point theorem to give Hyers-Ulam stability results for a nonlinear functional ...alternative theorem for Hyers-Ulam- Rassias stability, ...point theorem in generalized metric ... See full document

... normed spaces (see ...main theorem in []. The generalized Hyers-Ulam stability problem for the case of r = p + q =  was excluded in Corollary ... See full document

... of stability problems for functional equations is related to a question of Ulam [30] concerning the stability of group homomorphisms and affirmatively answered for Banach spaces ... See full document

... Banach spaces. In , Rassias [] ex- tended the theorem of Hyers by considering the unbounded Cauchy ...Hyers-Ulam-Rassias stability with the generalized control function. This stability ... See full document

... The stability problem of functional equations is originated from a question of Ulam 11 concerning the stability of group ...Banach spaces. Hyers’ theorem was generalized ... See full document

... the stability problems for cubic-quadratic-additive type functional equa- tions, we frequently encounter the cases where we should prove the uniqueness of the cubic-quadratic-additive mappings (see ... See full document

... The stability of several functional equations have been extensively investigated by a number of mathematicians and there are many interesting results concerning this problem (see [3, 4, 21, ... See full document

... For this reason, 1.1 is called a quartic functional equation. Also Chung and Sahoo 16 determined the general solution of 1.1 without assuming any regularity conditions on the unknown function. In fact, they ... See full document

... Lemma 3.1. A mapping f : X → Y satisfies (1.1) if and only if the mapping f : X → Y is quartic. Theorem 3.2. Let X be a linear space, (Y,N ) and (Z, N 0 ) be a fuzzy Banach space and a fuzzy normed ... 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 0 be a mapping between ... See full document

... for all x, y ∈ X. By taking s → ∞, the definition of Q implies that Q satisfies 1.4 for all x, y ∈ X; that is, Q is the generalized quartic mapping. Also, the inequality 3.8 implies the inequality 3.3. Now, it remains to ... 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 ) d J x J ( n ... See full document

... of stability problems for functional equations is related to a question of Ulams[24] concerning the stability of group homomorphism’s was affirmatively answered for Banach spaces ... See full document

... 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 [5], [6], [8], [16], ... See full document

... of fuzzy normed linear spaces. Fuzzy Sets ...XH: Fuzzy normed spaces of operators and its completeness. Fuzzy Sets ...AK: Fuzzy topological vector spaces II. ... See full document