An Iterative Algorithm for Approximating the Fixed Point of a Contractive Affine Operator
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MDPI
Materia
Iterative numerical methods Schauder bases Fredholm integral equation
Date
2022-03-22Referencia bibliográfica
Berenguer, M.I.; Ruiz Galán, M. An Iterative Algorithm for Approximating the Fixed Point of a Contractive Affine Operator. Mathematics 2022, 10, 1012. [https://doi.org/10.3390/math10071012]
Sponsorship
Junta de Andalucia FQM359; "Maria de Maeztu" Excellence Unit IMAG - MCIN/AEI CEX2020-001105-MAbstract
First of all, in this paper we obtain a perturbed version of the geometric series theorem,
which allows us to present an iterative numerical method to approximate the fixed point of a
contractive affine operator. This result requires some approximations that we obtain using the
projections associated with certain Schauder bases. Next, an algorithm is designed to approximate
the solution of Fredholm’s linear integral equation, and we illustrate the behavior of the method with
some numerical examples.