Results 41 to 50 of about 547 (94)
On a functional equation that has the quadratic-multiplicative property
Open Mathematics, 2020 In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation:ϕ(st−uv)+ϕ(sv+tu)=[ϕ(s)+ϕ(u)][ϕ(t)+ϕ(v)]\phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v ...
Park Choonkil +4 more
doaj +1 more source
On the Orthogonal Stability of the Pexiderized Quadratic Equation
, 2005 The Hyers--Ulam stability of the conditional quadratic functional equation of Pexider type f(x+y)+f(x-y)=2g(x)+2h(y), x\perp y is established where \perp is a symmetric orthogonality in the sense of Ratz and f is odd.Comment: 10 pages, Latex; Changed ...
Aczél J. +12 more
core +2 more sources
Picard and Adomian methods for quadratic integral equation
, 2010 We are concerning with two analytical methods; the classical method of successive approximations (Picard method) [14] which consists the construction of a sequence of functions such that the limit of this sequence of functions in the sense of uniform ...
A. El-Sayed, H. Hashem, E. Ziada
semanticscholar +1 more source
Approximate Homomorphisms of Ternary Semigroups
, 2005 A mapping $f:(G_1,[ ]_1)\to (G_2,[ ]_2)$ between ternary semigroups will be called a ternary homomorphism if $f([xyz]_1)=[f(x)f(y)f(z)]_2$. In this paper, we prove the generalized Hyers--Ulam--Rassias stability of mappings of commutative semigroups into ...
A. Cayley +22 more
core +2 more sources
On the generalized Hyers-Ulam-Rassias stability problem of radical functional equations
Journal of Inequalities and Applications, 2012 In this paper, the generalized Hyers-Ulam-Rassias stability problem of radical quadratic and radical quartic functional equations in quasi-β-Banach spaces and then the stability by using subadditive and subquadratic functions for radical functional ...
S. Kim, Y. Cho, M. Eshaghi Gordji
semanticscholar +1 more source
Hyers-Ulam stability of isometries on bounded domains-II
Demonstratio Mathematica, 2023 The question of whether there is a true isometry approximating the ε\varepsilon -isometry defined in the bounded subset of the nn-dimensional Euclidean space has long been considered an interesting question.
Choi Ginkyu, Jung Soon-Mo
doaj +1 more source
On a type of exponential functional equation and its superstability in the sense of Ger [PDF]
, 2013 In this paper, we deal with a type exponential functional equation as follows $$f(xy)=f(x)^{g(y)},$$ where $f$ and $g$ are two real valued functions on a commutative semigroup.
Alimohammady, M. +2 more
core
Approximate derivations of order $n$
, 2016 The aim of this paper is to prove characterization theorems for higher order derivations. Among others we prove that the system defining higher order derivations is stable.
Gselmann, Eszter
core +1 more source
Generalized Hyers-Ulam stability of Riccati differential equation
, 2008 In this paper, we will prove the generalized Hyers-Ulam stability of the Riccati differential equation of the form y′(t)+ g(t)y(t)+ h(t)y(t)2 = k(t) under some additional conditions. Some concrete examples will be introduced.
Soon-Mo Jung, T. Rassias
semanticscholar +1 more source
On the stability of J$^*-$derivations
, 2009 In this paper, we establish the stability and superstability of $J^*-$derivations in $J^*-$algebras for the generalized Jensen--type functional equation $$rf(\frac{x+y}{r})+rf(\frac{x-y}{r})= 2f(x).$$ Finally, we investigate the stability of $J ...
A. Ebadian +25 more
core +2 more sources