Fixed-Point Methods for a Certain Class of Operators |
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Authors: | Rolando Gárciga Otero Alfredo Iusem |
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Institution: | 1. Instituto de Economia da Universidade Federal de Rio de Janeiro, Avenida Pasteur 250, Urca, Rio de Janeiro, RJ, 22290-240, Brazil 2. Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil
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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. |
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