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On Strong Convergence of Halpern’s Method for Quasi-Nonexpansive Mappings in Hilbert Spaces

    Jesus Garcia Falset Affiliation
    ; Enrique Llorens-Fuster Affiliation
    ; Giuseppe Marino Affiliation
    ; Angela Rugiano Affiliation

Abstract

In this paper, we introduce a Halpern’s type method to approximate common fixed points of a nonexpansive mapping T and a strongly quasi-nonexpansive mappings S, defined in a Hilbert space, such that I − S is demiclosed at 0. The result shows as the same algorithm converges to different points, depending on the assumptions of the coefficients. Moreover, a numerical example of our iterative scheme is given.

Keyword : approximation algorithm, fixed point, variational inequality

How to Cite
Falset, J. G., Llorens-Fuster, E., Marino, G., & Rugiano, A. (2016). On Strong Convergence of Halpern’s Method for Quasi-Nonexpansive Mappings in Hilbert Spaces. Mathematical Modelling and Analysis, 21(1), 63-82. https://doi.org/10.3846/13926292.2016.1132787
Published in Issue
Jan 26, 2016
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