Results 221 to 230 of about 7,083 (231)

Generalized Hyers–Ulam Stability of a Quadratic Functional Equation

, 2011
Let a be a fixed integer with a≠−1,0. We obtain the general solution and the generalized Hyers–Ulam stability theorem for a quadratic functional equation $$\begin{array}{rcl} f(ax + y) + af(x - y) = (a + 1)f(y) + a(a + 1)f(x).& & \\ \end{array}$$
K. Jun, Hark-Mahn Kim, Ji A Son
semanticscholar   +2 more sources

On Hyers--Ulam stability of the generalized Cauchy and Wilson equations

Publicationes Mathematicae Debrecen, 2005
Let \(G\) be a topological group and \(\mu\) a compactly supported measure on \(G\). Moreover, let \(\sigma\) denote a continuous involution on \(G\). The authors consider the following functional equations: \[ \begin{aligned} &\int_G f(xty) d\mu(t)=g(x)f(y),\\ &\int_G f(xty) d\mu(t)+\int_G f(xt\sigma(y)) d\mu(t)=2f(x)g(y).\\ \end{aligned} \] The first
Elqorachi, Elhoucien, Akkouchi, Mohamed
openaire   +1 more source

Hyers–Ulam stability of generalized Wilson’s and d’Alembert’s functional equations

Afrika Matematika, 2013
The authors investigate the Hyers-Ulam stability for the following functional equation \[ \sum_{\varphi \in \Phi} \int_K f(xk\varphi(y)k^{-1})\;dw_K(k)=|\Phi|f(x)g(y), \quad x,y \in G, \leqno (E) \] where \(G\) is a locally compact group, \(K\) is a compact subgroup of \(G\), \(w_K\) is the normalized Haar measure of \(K\), \(\Phi\) is a finite group ...
Zeglami, D., Roukbi, A., Kabbaj, S.
openaire   +2 more sources

On Hyers–Ulam stability of generalized linear functional equation and its induced Hyers–Ulam programming problem

Aequationes mathematicae, 2015
The Hyers-Ulam stability of a generalized linear functional equation is investigated. The connection between the existence of a solution of a certain inequality and the stability problem is also examined.
openaire   +2 more sources

A generalization of the Hyers--Ulam--Rassias stability of the beta functional equation

Publicationes Mathematicae Debrecen, 2001
A functional equation \(E[h]=0\) is Hyers-Ulam-Rassias(-Găvruta)-stable if, given a function \(\phi,\) there exists a function \(\Phi\) such that \(|E[f]|\leq\phi\) implies the existence of a unique \(g\) for which \(E[g]=0\) and \(|f-g|\leq\Phi\); cf. \textit{D. H. Hyers} [Proc. Nat. Acad. Sci. U.S.A. 27, 222-224 (1941; Zbl 0061.26403)], \textit{S. M.
openaire   +1 more source

A new method for the generalized Hyers-Ulam-Rassias stability

2010
We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.
Gavruta, P., Gavruta, L.
openaire   +1 more source

Generalized Hyers–Ulam stability of an Euler–Lagrange type additive mapping

, 2006
Choonkill Park, Jae Myoung Park
semanticscholar   +1 more source

Generalized Hyers-Ulam stability of a general mixed additive-cubic functional equation in quasi-Banach spaces

, 2012
Tianzhou Xu, J. Rassias, W. Xu
semanticscholar   +1 more source

Generalized Hyers-Ulam Stability for a General Mixed Functional Equation in Quasi-β-normed Spaces

, 2011
G. Z. Eskandani, P. Gǎvruţa, J. Rassias, R. Zarghami   +3 more
semanticscholar   +1 more source

GENERALIZED HYERS-ULAM STABILITY FOR A GENERAL CUBIC FUNCTIONAL EQUATION IN QUASI-β-NORMED SPACES

, 2011
G. Eskandani, J. Rassias, P. Gǎvruţa
semanticscholar   +1 more source