Results 11 to 20 of about 814 (188)

On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations [PDF]

Abstract and Applied Analysis, 2009
We achieve the general solution and the generalized Hyers‐Ulam‐Rassias and Ulam‐Gavruta‐Rassias stabilities for quadratic functional equations f(ax + by) + f(ax − by) = (b(a + b)/2)f(x + y) + (b(a + b)/2)f(x − y) + (2a2 − ab − b2)f(x) + (b2 − ab)f(y) where a, b are nonzero fixed integers with b ≠ ±a, −3a, and f(ax + by) + f(ax − by) = 2a2f(x) + 2b2f(y)
M‎. ‎Eshaghi Gordji, H. Khodaei
openalex   +6 more sources

Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras [PDF]

Fixed Point Theory and Applications, 2007
We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: , , which were introduced and investigated by Baak (2006 ...
Park Choonkil
doaj   +3 more sources

Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras

Journal of Inequalities and Applications, 2005
We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras.
Takeshi Miura, Sin‐Ei Takahasi, Go Hirasawa   +2 more
openalex   +4 more sources

Stability analysis and solutions of fractional boundary value problem on the cyclopentasilane graph [PDF]

Heliyon
The study is being applied to a model involving silane and on cyclopentasilane graph. We consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of cyclopentasilane. In this paper, we first study the existence of solutions to
Guotao Wang, Hualei Yuan, Dumitru Baleanu   +2 more
doaj   +2 more sources

HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION [PDF]

Bulletin of the Korean Mathematical Society, 2003
Let \(X\) and \(Y\) be real vector spaces. One of main theorems of this paper states that a function \(f: X\to Y\) satisfies the functional equation \[ n^2{n-2\choose k-2}\, f\Biggl({x_1+\cdots+ x_n\over n}\Biggr)+ {n-2\choose k-1}\,\sum^n_{i=1} f(x_i)= k^2 \sum_{1\leq ...
Тибериу Триф
openalex   +5 more sources

Stability of some generalized fractional differential equations in the sense of Ulam-Hyers-Rassias. [PDF]

Bound Value Probl, 2023
Makhlouf AB, El-Hady ES, Arfaoui H, Boulaaras S, Mchiri L.   +4 more
europepmc   +3 more sources

Hyers–Ulam–Rassias Stability of a Jensen Type Functional Equation

Journal of Mathematical Analysis and Applications, 2000
The author studies the Hyers-Ulam-Rassias stability of a Jensen type functional equation \[ 3f((x+y+z)/3)+ f(x)+ f(y)+ f(z)= 2[ f((x+y)/2)+ f((y+z)/2)+ f((z+x)/2)]. \] The main result of this paper is the following: If the function \(f: X\to Y\) satisfies \[ \begin{multlined}\|3 f((x+y+z)/3)+ f(x)+ f(y)+ f(z)- 2[f((x+y)/2)+ f((y+z)/2)+ f((z+x)/2)]\|\\ \
Тибериу Триф
openalex   +3 more sources

Some Further Generalizations of the Hyers–Ulam–Rassias Stability of Functional Equations

Journal of Mathematical Analysis and Applications, 2001
Let \(G\neq\emptyset\) be a set with a binary operation \(x\ast y\in G\) such that the left powers (\(x^1=x\), \(x^{m+1}=x\ast x^m\)) satisfy \(x^{m+n}=x^m\ast x^n\) for all \(m,n\in\mathbb N\) and all \(x\in G\). Such a set \(G\) is called a power-associative groupoid [cf. \textit{J. Rätz}, General inequalities 2, ISNM Vol. 47, 233-251 (1980; Zbl 0433.
Jian Wang
openalex   +3 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.
Gwang Hui Kim
openalex   +3 more sources

On the stability of first order impulsive evolution equations [PDF]

Opuscula Mathematica, 2014
In this paper, concepts of Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for impulsive evolution equations are raised.
JinRong Wang, Michal Fečkan, Yong Zhou
doaj   +1 more source