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Isomorphisms, Schauder bases in Banach spaces, and numerical solution of integral and differential equations. (English) Zbl 1079.65067

In the first part of the paper the authors approximate the fixed point of an isomorphism between two Banach spaces, one of them possessing a Schauder basis, using a sequence of best approximations in finite-dimensional spaces generated by this basis. They apply their results to some Volterra integral equations. Numerical examples illustrate the theoretical assertions.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
65R20 Numerical methods for integral equations
47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
45G10 Other nonlinear integral equations
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References:

[1] Deville R., Pitman Monographs and Surveys in Pure and Applied Mathematics 64, in: Smoothness and Renormings in Banach Spaces. (1993) · Zbl 0782.46019
[2] DOI: 10.1007/978-1-4612-0603-3 · Zbl 0910.46008
[3] Pedersen G. K., Analysis Now (1995) · Zbl 0668.46002
[4] Schechter E., Handbook of Analysis and Its Foundations (1997) · Zbl 0943.26001
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