[PDF] Top 20 On the Stability of a New Pexider Type Functional Equation

... which is mixed of a quadratic and an additive functional equations. In this paper, we establish the generalized Hyers-Ulam-Rassias stability for 1.6 on the punctured domain V \ {0} and obtain its general ... 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

... Sikorska, Stability of the orthogonal additivity, ...the stability of the linear functional equation, ...Quadratic functional equation inner product spaces, Results ...orthogonal ... 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

... 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

... F ( R ) → S ( R ), S ( R ) → F ( R ). (2 : 3) Taking the relations (2.3) into account, it suffices to consider the space F ( R ) . In order to solve the general solution and the stability problem of (1.2) in the ... See full document

... If the problem accepts a solution, we say that the equation is stable. The first sta- bility problem concerning group homomorphisms was raised by Ulam [35] in 1940. In the next year, Hyres [11] gave a positive ... 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

... 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

... of stability theory of functional equations for the proof of new fixed point theorems with ...the stability problems of several functional equations have been extensively investigated by ... 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

... the functional equation f x y f xfy was studied by Baker et ...a functional on a real vector space W satisfying |fx y − f xfy| ≤ δ for some fixed δ > 0 and all x, y ∈ W , then f is either bounded ... See full document

... on Functional Equations asked the question whether such a theorem can also be proved for p ≥ ...Rassias’ type theorem when p = ...invent new approximately additive or approximately linear ...similar ... 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

... 5. Solutions of equation (1.7). We will now solve the functional equation (1.7) which is a “pexiderized” form of (1.4) in the class of functions between vector spaces. Theorem 5.1. Assume that X and ... See full document

... In papers Acz´el 22, Acz´el and Dhombres 23, Kannappan 24, 25, and Kim and Kannappan 13, we can find that the Wilson equation and the sine equations can be represented by the composition of a homomorphism. By ... See full document

... the stability problem of functional equations has been extended in various directions and studied by several mathematicians (see [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...Hyers-Ulam stability of the Hossz¨ ... 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

... of functional equations is as ...a functional equation must be close to an exact solution of the equation?” The first stability problem concerning group homomorphisms was raised by Ulam ... 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