Results 101 to 110 of about 1,516 (136)

On the qualitative behaviors of Volterra-Fredholm integro differential equations with multiple time-varying delays

Arab Journal of Basic and Applied Sciences
This article considers a Volterra-Fredholm integro-differential equation including multiple time-varying delays. The aim of this article is to study the uniqueness of solution, the Ulam–Hyers–Rassias stability and the Ulam–Hyers stability of the Volterra-
Cemil Tunç, Osman Tunç
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On Ulam Stability of an Operatorial Equation

Mediterranean Journal of Mathematics, 2021
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Delia-Maria Kerekes, Dorian Popa
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Generalized Dichotomies and Hyers–Ulam Stability

Results in Mathematics, 2023
Consider \[ x^\prime=A(t)x+f(t,x),\,t\geq 0,\tag{1} \] where \(A:\mathbb{R}_+\to \mathbb{R}^{n\times n}\) and \(f:\mathbb{R}_+\times \mathbb{R}^n\to \mathbb{R}^n\) are continuous mappings. It is known that if the corresponding linear differential equation \(x^\prime=A(t)x\) has a uniform exponential dichotomy and \(f(t,x)\) is Lipschitz in \(x ...
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SOLUTION OF A STABILITY PROBLEM OF ULAM

1994
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On the Stability of Functional Equations and a Problem of Ulam

Acta Applicandae Mathematica, 2000
In 1940 S.~M.~Ulam posed the problem concerning the stability of homomorphisms. In 1941 D.~H.~Hyers gave the first significant partial solution: Let \(X,Y\) be Banach spaces and \(\delta>0\). If the function \(f:X\to Y\) satisfies the inequality \[ \bigl\|f(x+y)-f(x)-f(y)\bigr\|\leq\delta\tag{\(\ast\)} \] for all \(x,y\in X\), then there exists the ...
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Ulam–Hyers stability of fractional Langevin equations

Applied Mathematics and Computation, 2015
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Jin Rong Wang 0001, Xuezhu Li
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On the Hyers–Ulam Stability of Bernoulli’s Differential Equation

Russian Mathematics
The aim of this paper is to present the results on the Hyers–Ulam–Rassias stability and the Hyers–Ulam stability for Bernoulli's differential equation. The argument makes use of a fixed point approach. Some examples are given to illustrate the main results.
Shah, R., Irshad, N.
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Ulam Stability Problem for Frames

2011
In this paper we give a solution to the Ulam stability problem for continuous Parseval frames in finite dimensional Hilbert spaces. We prove that if F is a nearly Parseval frame then there exists a Parseval frame near F. Also, we give generalizations of this result.
Laura Găvruţa, Paşc Găvruţa
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On Ulam Stability in the Geometry of PDE’s

2003
The article is concerned with the problem of the unstability of flows corresponding to solutions of the Navier—Stokes equation in relation with the stability of a new functional equation (functional Navier—Stokes equation),that is stable as well as superstable in an extended Ulam sense.
Agostino Prástaro, Themistocles M. Rassias   +1 more
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Ulam stability in geometry of PDE's

2003
The concept of Hyers-Ulam-Rassias stability is applied to the Navier-Stokes equation. In the first part of the paper the geometric formulation of the Navier-Stokes equation as introduced by A.~Prástaro is recalled. The second part contains a~short account on the stability of functional equations.
PRASTARO, Agostino, RASSIAS T.H. M.
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