[PDF] Top 20 Stability of an additive functional equation in the spaces of generalized functions

... was proposed by Nakmahachalasint [14], where n is a positive integer with n > 1. He proved that (1.2) is equivalent to (1.1). For that reason, we say that (1.2) is a generali- zation of the Cauchy functional ... See full document

... quadratic functional equation: f xy z fx fy fz fx y fy z fz x in the spaces of generalized ...heat equation, we obtain the general solution and prove the Hyers-Ulam stability of ... See full document

... Ulam stability problem: When is it true that by slightly changing the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true? In [19], Hyers gave the first ... See full document

... If p < 0 or q < 0, the right-hand side of (1.7) does not define a distribution and so inequality (1.7) makes no sense. If p,q = 3, it is not guaranteed whether Hyers-Ulam- Rassias stability of (1.5) is hold ... See full document

... the generalized Hyers-Ulam-Rassias sta- bility for a mixed type of quadratic and additive functional ...Hyers-Ulam-Rassias stability for a mixed type of cubic, quadratic and additive ... See full document

... the generalized Hyers- Ulam stability of the functional equation ...Banach spaces for an even case. In Section 4, we prove the generalized Hyers-Ulam stability of the ... See full document

... The stability problem of functional equations was originated from a question of Ulam 1 concerning the stability of group ...Banach spaces. Hyers’ theorem was generalized by Aoki 3 for ... See full document

... f (x + y) + f (x − y) = 2f(x) + 2f (y) (1.1) is related to a symmetric bi-additive function [30, 31]. It is natural that this equa- tion is called a quadratic functional equation. In particular, ... See full document

... the additive mapping h, was called a direct ...the stability of various functional ...for additive mappings by considering an unbounded Cauchy ...Banach spaces and f : E 1 ... See full document

... of stability theory of functional equations for the proof of new fixed-point theorems with applica- ...the stability problems of several functional equations have been extensively investigated ... See full document

... the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation f x 2y f x − 2y 2f x y 2f − x − y 2fx − y 2f y − x − 4f−x − 2fx f2y f−2y − 4fy − ... See full document

... G˘avrut¸a [10] provided a further generalization of Rassias’ theorem. During the last two decades, a number of papers and research monographs have been published on vari- ous generalizations and applications of 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

... the stability problem of functional equations which was first raised by ...Banach spaces. A generalized version of the theorem of Hyers for approximately linear mappings was given by ... 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) - ... See full document

... the stability of functional equations on Banach ...The generalized version of ...The stability paper [12] given by ...of stability of functional ... 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 stability for the ... See full document

... 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 ...is additive for fixed two ... See full document

... (3.1.30) for all v ∈ U and all y ∈ U . The rest of the proof is similar to that of Theorem 3.1.1.The following corollary is an immediate consequence of Theorem 3.1.2 concerning the stability of (1.1). ... See full document

... following generalized additive functional inequality afx bfy cfz ≤ fαx βy γz, associated with linear mappings in Banach ...Hyers-Ulam-Rassias stability of the above generalized ... See full document