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An Iterative Algorithm for Approximating the Fixed Point of a Contractive Affine Operator

Author

Listed:
  • María Isabel Berenguer

    (Department of Applied Mathematics, E.T.S. Ingeniería de Edificación, University of Granada, 18071 Granada, Spain
    Institute of Mathematics (IMAG), University of Granada, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Manuel Ruiz Galán

    (Department of Applied Mathematics, E.T.S. Ingeniería de Edificación, University of Granada, 18071 Granada, Spain
    Institute of Mathematics (IMAG), University of Granada, 18071 Granada, Spain
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • María Isabel Berenguer & Manuel Ruiz Galán, 2022. "An Iterative Algorithm for Approximating the Fixed Point of a Contractive Affine Operator," Mathematics, MDPI, vol. 10(7), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1012-:d:776614
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    References listed on IDEAS

    as
    1. Karimi, Saeed & Jozi, Meisam, 2015. "A new iterative method for solving linear Fredholm integral equations using the least squares method," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 744-758.
    2. Yonghong Yao & Mihai Postolache & Jen-Chih Yao, 2019. "An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems," Mathematics, MDPI, vol. 7(1), pages 1-15, January.
    3. Cominola, A. & Giuliani, M. & Piga, D. & Castelletti, A. & Rizzoli, A.E., 2017. "A Hybrid Signature-based Iterative Disaggregation algorithm for Non-Intrusive Load Monitoring," Applied Energy, Elsevier, vol. 185(P1), pages 331-344.
    4. S. Saha Ray & P. K. Sahu, 2013. "Numerical Methods for Solving Fredholm Integral Equations of Second Kind," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-17, December.
    5. Alipour, Sahar & Mirzaee, Farshid, 2020. "An iterative algorithm for solving two dimensional nonlinear stochastic integral equations: A combined successive approximations method with bilinear spline interpolation," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    Full references (including those not matched with items on IDEAS)

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