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Applications of Banach Limit in Ulam Stability [PDF]

Symmetry, 2021
We show how to get new results on Ulam stability of some functional equations using the Banach limit. We do this with the examples of the linear functional equation in single variable and the Cauchy equation.
Roman Badora, Janusz Brzdęk, Krzysztof Ciepliński   +2 more
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On Ulam Stability of an Operatorial Equation

Mediterranean Journal of Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Delia-Maria Kerekes, Dorian Popa
openaire   +1 more source

The Hyers–Ulam stability of nonlinear recurrences

Journal of Mathematical Analysis and Applications, 2007
In the paper of \textit{D. Popa} [J. Math. Anal. Appl. 309, No. 2, 591--597 (2005; Zbl 1079.39027)] the Hyers-Ulam stability problem was proved for linear recurrences in a Banach space. In the paper under review, the authors investigate this problem for nonlinear recurrences in a metric space \((X, d)\). More precisely, they show that if \(\{x_n\}\), \(
Janusz Brzdęk, Dorian Popa
exaly   +2 more sources

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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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