An Iterative Algorithm for Approximating the Fixed Point of a Contractive Affine Operator Berenguer Maldonado, María Isabel Ruiz Galán, Manuel Iterative numerical methods Schauder bases Fredholm integral equation This research was partially supported by Junta de Andalucia, Project "Convex and numerical analysis", reference FQM359, and by the "Maria de Maeztu" Excellence Unit IMAG, reference CEX2020-001105-M, funded by MCIN/AEI/10.13039/501100011033/. 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. 2022-05-04T06:45:08Z 2022-05-04T06:45:08Z 2022-03-22 journal article 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] http://hdl.handle.net/10481/74673 10.3390/math10071012 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España MDPI