Journal ArticleDOI
On the Stability of Functional Equations and a Problem of Ulam
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In this article, the stability of functional equations has been studied from both pure and applied viewpoints, and both classical results and current research are presented in a unified and self-contained fashion.Abstract:
In this paper, we study the stability of functional equations that has its origins with S. M. Ulam, who posed the fundamental problem 60 years ago and with D. H. Hyers, who gave the first significant partial solution in 1941. In particular, during the last two decades, the notion of stability of functional equations has evolved into an area of continuing research from both pure and applied viewpoints. Both classical results and current research are presented in a unified and self-contained fashion. In addition, related problems are investigated. Some of the applications deal with nonlinear equations in Banach spaces and complementarity theory.read more
Citations
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The fixed point alternative and the stability of functional equations
TL;DR: In this article, it was shown that the theorems of Hyers, Rassias and Gajda concerning the stability of the Cauchy's functional equation in Banach spaces are direct consequences of the alternative of fixed point.
Journal Article
Fixed points and the stability of jensens functional equation
L Cadariu,V Radu +1 more
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Hyers-Ulam stability of linear differential equations of first order
TL;DR: Using the method of the integral factor, this work proves the Hyers–Ulam stability of linear differential equations of first order and extends the existing results.
Journal ArticleDOI
Homomorphisms between Poisson JC*-Algebras
TL;DR: The stability of Poisson JC*-algebra homomorphisms was shown in this article, where it was shown that the Cauchy-Rassias stability of poisson JC*, algebras can be maintained.
References
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Journal ArticleDOI
On the Stability of the Linear Functional Equation
TL;DR: This program includes in particular the complete theory of the convergence and divergence of formal series, the explicit determination of the essential transcendental invariants, the inverse Riemann theory both for the neighborhood of x = o and in the complete plane, explicit integral representation of the solutions, and finally the definition of q-sigma periodic matrices.
Book
The Linear Complementarity Problem
TL;DR: In this article, the authors present an overview of existing and multiplicity of degree theory and propose pivoting methods and iterative methods for degree analysis, including sensitivity and stability analysis.
Journal ArticleDOI
On the stability of the linear mapping in Banach spaces
TL;DR: In this article, the authors give an answer to Ulam's problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist", and prove it for the case n = 1.