Results 81 to 90 of about 814 (188)

Improved Stability and Instability Results for Neutral Integro‐Differential Equations including Infinite Delay

Journal of Mathematics, Volume 2024, Issue 1, 2024.
In this article, we consider nonlinear neutral Volterra integro‐differential equations (NVIDEs) including infinite delay. We prove three new theorems with regard to the stability, the uniform stability, and the instability of zero solution of the NVIDEs.
Cemil Tunç, Fahir Talay Akyildiz, Valerii Obukhovskii   +2 more
wiley   +1 more source

Stability Results for a Class of Fractional Itô–Doob Stochastic Integral Equations

Complexity, Volume 2024, Issue 1, 2024.
In this paper, we study the Hyers–Ulam stability of Hadamard fractional Itô–Doob stochastic integral equations by using the Banach fixed point method and some mathematical inequalities. Finally, we exhibit three theoretical examples to apply our theory.
Omar Kahouli, Ali Aloui, Lassaad Mchiri, Abdellatif Ben Makhlouf, Daniel Maria Busiello   +4 more
wiley   +1 more source

On the Aleksandrov-Rassias problem and the Hyers-Ulam-Rassias stability problem [PDF]

Banach Journal of Mathematical Analysis, 2007
Let X and Y be normed linear spaces. A mapping T : X ! Y is called preserving the distance r if for all x,y of X with kx ykX = r then kT(x) T(y)k = r. In this paper, we provide an overall account of the development of the Aleksandrov problem, the Aleksandrov-Rassias problem for mappings which preserve distances and details for the Hyers-Ulam-Rassias ...
Tan, Liyun, Xiang, Shuhuang
openaire   +2 more sources

Approximate Controllability and Ulam Stability for Second‐Order Impulsive Integrodifferential Evolution Equations with State‐Dependent Delay

International Journal of Differential Equations, Volume 2024, Issue 1, 2024.
In this paper, we shall establish sufficient conditions for the existence, approximate controllability, and Ulam–Hyers–Rassias stability of solutions for impulsive integrodifferential equations of second order with state‐dependent delay using the resolvent operator theory, the approximating technique, Picard operators, and the theory of fixed point ...
Abdelhamid Bensalem, Abdelkrim Salim, Mouffak Benchohra, Gaston N’Guérékata, Amar Nath Chatterjee   +4 more
wiley   +1 more source

On the Stability of a Cubic Functional Equation in Random Normed Spaces

Journal of Mathematical Extension, 2009
The concept of Hyers-Ulam-Rassias stability has been originated from a stability theorem due to Th. M. Rassias. Recently, the Hyers-Ulam-Rassias stability of the functional equation f(x + 2y) + f(x − 2y) = 2f(x) − f(2x) + 4n f(x + y) + f(x − y) o ,
H. Azadi Kenary
doaj  

Stability of the Cauchy-Jensen Functional Equation in C∗-Algebras: A Fixed Point Approach

Fixed Point Theory and Applications, 2008
we prove the Hyers-Ulam-Rassias stability of C∗-algebra homomorphisms and of generalized derivations on C∗-algebras for the following Cauchy-Jensen functional equation 2f((x+y)/2+z)=f(x)+f(y)+2f(z), which was introduced and investigated by Baak
Jong Su An, Choonkil Park
doaj   +1 more source

On Hyers-Ulam-Rassias Stability of a Volterra-Hammerstein Functional Integral Equation

, 2022
The aim of this paper is to study Hyers-Ulam-Rassias stability for a Volterra-Hammerstein functional integral equation in three variables via Picard operators.
Ciplea, Sorina Anamaria, Lungu, Nicolaie, Marian, Daniela, Rassias, Themistocles M.   +3 more
openaire   +2 more sources

Study on existence and stability analysis for implicit neutral fractional differential equations of ABC derivative

Partial Differential Equations in Applied Mathematics
In this paper, we study the existence, uniqueness, and stability analysis of non-linear implicit neutral fractional differential equations involving the Atangana–Baleanu derivative in the Caputo sense. The Banach contraction principle theorem is employed
V. Sowbakiya, R. Nirmalkumar, K. Loganathan, C. Selvamani   +3 more
doaj   +1 more source

On the Hyers–Ulam–Rassias stability of functional equations in n-variables

Journal of Mathematical Analysis and Applications, 2004
In this interesting paper the author proves the stability in the sense of Hyers-Ulam-Rassias and Găvruţa for the functional equation \[ f(\varphi(X))=\phi(X)f(X)+\psi(X) \] and the stability in the sense of R. Ger for the functional equation \[ f(\varphi(X))=\phi(X)f(X), \] where \(X\) lies in \(n\)-variables. Some applications are given.
openaire   +3 more sources

Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras

Banach Journal of Mathematical Analysis, 2007
AbstractIn this paper, we prove the Hyers–Ulam–Rassias stability of homomorphisms in quasi-Banach algebras. This is applied to investigate isomorphisms between quasi-Banach algebras.
openaire   +4 more sources