[PDF] Top 20 Hyperstability and Stability of a Logarithm type Functional Equation

... In next year, Hyers [11] proved a first partial answer to Ulam’s problem for an additive mapping on a Banach space. D. G. Bourgin obtained many excellent results for the stability ([3], [4]).Hyers’ theorem was ... See full document

... Holling type- III functional response in the Caputo sense by modifying model ...local stability of the equilibria for the model using the linearization ... See full document

... 3. The modified Hyers-Ulma-Rassias stability of g(x + p) = ϕ(x)g(x). In this section, we investigate the modified Hyers-Ulam-Rassias stability for equations of the form (1.3) in two types. The former (Theorem ... See full document

... for all x ∈ E. Moreover if f tx is continuous in t for each fixed x ∈ E, then T is linear see also 3. In 1950, Aoki 4 generalized Hyers’ theorem for approximately additive mappings. In 1978, Th. M. Rassias 5 provided a ... 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. ... See full document

... on Functional Equations asked the question whether such a theorem can also be proved for p ...Hyers-Ulam stability concept. This new concept of stability is known as general- ized Hyers-Ulam ... See full document

... Rassias [9] followed the innovative approach of Rassias ’ theorem [3] in which he replaced the factor ∥ x ∥ p + ∥ y ∥ p by ∥ x ∥ p · ∥ y ∥ q for p,q Î ℝ with p + q ≠ 1. G ă vruta [10] provided a further generalization of ... See full document

... of stability problems for functional equations has originally been raised by Ulam []: under what condition does there exist a homomorphism near an approximate homomorphism? In , Hyers [] had answered ... See full document

... Katsaras 1 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 2–4. In ... 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 ... See full document

... The stability problem of functional equations originated from a question of Ulam [1] concerning the stability of group ...Hyers-Ulam stability of func- tional ... See full document

... Hyers-Ulam stability problems of functional equations go back to 1940 when Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group (see ...numerous functional ... See full document

... on Functional Equations asked the question whether such a theorem can also be proved for p ≥ ...Rassias’ type theorem when p = ...similar stability theorem in which he replaced the unbounded Cauchy ... See full document

... functional equation. In particular, every solution of the qua- dratic functional equation is said to be a quadratic ...Hyers-Ulam stability problem for the quadratic functional ... See full document

... In this article, we consider equation (1.1) in the spaces of generalized functions such as the space S (R) of tempered distributions and the space F (R) of Fourier hyperfunc- tions. Making use of similar ... See full document

... An inquisitive question that was given a serious thought by S.M. Ulam [42] concerning the stability of group homomorphisms gave rise to the stability problem of functional equations. The laborious ... See full document

... Hyers-Ulam stability of the Cauchy expo- nential equation f (x + y) = f (x)f ...the functional inequality f (xy) – f (x)f (y) ≤ δ for all x, y ∈ S, then f is either bounded or ... See full document

... functional equation. In particular, every solution of the quadratic functional equation is said to be quadratic ...of stability theory of functional equations for the proof of ... See full document

... the stability of the linear functional ...the stability of the linear mapping in Banach ...S: Functional Equations and Inequalities in Several ...Hyers-Ulam-Rassias stability of ... See full document

... (x)} starting from a given mapping f , which converges to the desired mapping F in the fuzzy sense. As we mentioned before, in previous studies of stability problem of (1.3), they attempted to get stability ... See full document