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Fixed-Point Methods for a Certain Class of Operators

Author

Listed:
  • Rolando Gárciga Otero

    (Instituto de Economia da Universidade Federal de Rio de Janeiro)

  • Alfredo Iusem

    (Instituto de Matemática Pura e Aplicada)

Abstract

We introduce in this paper a new class of nonlinear operators, which contains, among others, the class of operators with semimonotone additive inverse and also the class of nonexpansive mappings. We study this class and discuss some of its properties. Then we present iterative procedures for computing fixed points of operators in this class, which allow for inexact solutions of the subproblems and relative error criteria. We prove weak convergence of the generated sequences in the context of Hilbert spaces. Strong convergence is also discussed.

Suggested Citation

  • Rolando Gárciga Otero & Alfredo Iusem, 2013. "Fixed-Point Methods for a Certain Class of Operators," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 656-672, December.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:3:d:10.1007_s10957-012-0146-y
    DOI: 10.1007/s10957-012-0146-y
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