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- Title
Convergence Criteria for Fixed Point Problems and Differential Equations.
- Authors
Sofonea, Mircea; Tarzia, Domingo A.
- Abstract
We consider a Cauchy problem for differential equations in a Hilbert space X. The problem is stated in a time interval I, which can be finite or infinite. We use a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we establish convergence criteria for both a general fixed point problem and the corresponding Cauchy problem. These criteria provide the necessary and sufficient conditions on a sequence { u n } , which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.
- Subjects
DIFFERENTIAL equations; CAUCHY problem; NONLINEAR operators; HILBERT space; DIFFERENTIABLE functions; VISCOELASTICITY
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 3, p395
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12030395