[PDF] Top 20 A Functional Equation of Aczél and Chung in Generalized Functions

... regularizing functions as in 7, 8, we consider the regularity of the solutions of ...for functional equation in Schwartz distribution 7, ...of functional equations, we refer the reader to 6, ... See full document

... For this reason, 1.1 is called a quartic functional equation. Also Chung and Sahoo 11 determined the general solution of 1.1 without assuming any regularity conditions on the unknown function. In ... See full document

... Copyright © 2007 Y.-S. Lee and S.-Y. Chung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, dis- tribution, and reproduction in any ... See full document

... Hyers-Ulam-Rassias stability problem for the quadratic functional equation (1.1) was first treated by F. Skof for functions f : A → B where A is a normed space and B is a Banach space (see [17]). ... See full document

... heat equation, we solve the general solutions and the stability problems of the above equation in the spaces of tempered distributions and Fourier ...regularizing functions, we extend these results ... See full document

... of functions f : A → B, where A is a normed space and B is a Banach ...several functional equations have been extensively investigated by a number of scholars, possed with creative thinking and critial dis- ... See full document

... of functional equations which are mostly based on the Cauchy additive func- tional equation of the form f (x +y) = f (x) + f (y), the classical quadratic functional equation f (x + y) + f (x – ... See full document

... u, v, respectively. Now we can apply Lemma 3.6. First assume that 3.29 holds and consider the cases i, ii, iii, and iv of Lemma 3.6. For the case i, it follows from 30, Page 61, Theorem 1 that the initial values u, v of ... See full document

... 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- ...reformulate equation (1.1) and the ... 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 this ... See full document

... a functional equation arises when one replaces a func- tional equation by an inequality which acts as a perturbation of the ...was generalized by Aoki [1] for approximate additive function and ... See full document

... 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

... The definitions and facts which we now give are necessary for understanding the following. We define C ? := C \ {0}, and when we talk about the complex number w 0 we always mean that w 0 ∈ C ? . By E we denote the set of ... See full document

... the functional equation f(pr,qs) + f(ps, qr) = f (p, q)f (r,s), which arises in the characterization of symmetrically compositive sum-form distance measures, and as products of some multiplicative ... See full document

... Remark 3.5 According to Definition 3.1, If θ = I, I is identity mapping on A , then a gen- eralized θ -derivation is a generalized derivation. If the mapping h is identity mapping and α = 2, Then Theorem 3.1 and ... See full document

... is given where σ is an involution of the normed space E and k is a fixed positive integer. Furthermore we investigate the Hyers-Ulam-Rassias stability of the func- tional equation. The Hyers-Ulam stability on ... See full document

... Difference equation and their associated operators not only play a role in their own right as direct mathematical models of physical phenomena but also provide the field of numerical analysis with powerful ... See full document

... If we set k = , then from Theorem . we obtain the following sharpened and generalized version of Aczél-Vasić-Pečarić inequality .. In particular, if we set p + q ≤ , then from Cor[r] ... See full document

... the generalized Hyers- Ulam stability of A-quadratic mappings in Banach A-modules associated with the functional equation ...of functional equations for the proof of new fixed point theorems ... See full document

... During the last three decades, a number of papers and research monographs have been published on various generalizations and applications of the generalized Hyers-Ulam sta- bility to a number of functional ... See full document