Iterative methods for the computation of fixed points of demicontractive mappings

Authors:
Charles E. Chidume;Ştefan Mruşter
Affiliations:
International Centre for Theoretical Physics, Trieste, Italy;West University of Timişoara, Timişoara, Romania
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

This paper surveys some of the main convergence properties of the Mann-type iteration for the demicontractive mappings. Some variants of the Mann iteration that ensure the strong convergence, like the (CQ) algorithm and a variant for the asymptotically demicontractive mappings are also considered. The usual framework of our study is a (real) Hilbert space and only to a certain extent some particular Banach spaces. Historical aspects are pointed out and some applications for the convex feasibility problem are discussed.