${\cal T}$-class algorithms for pseudocontractions and $κ$-strict pseudocontractions in Hilbert spaces

Details ${\cal T}$-class algorithms for pseudocontractions and $κ$-strict pseudocontractions in Hilbert spaces ${\cal T}$-class algorithms for pseudocontractions and $κ$-strict pseudocontractions in Hilbert spaces

2007-12-04

arxiv.org/abs/0712.0528v1

Mathematics

Optimization and Control

Scientific paper

In this paper we study iterative algorithms for finding a common element of the set of fixed points of $\kappa$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous mapping. The last problem being related to finding fixed points of pseudocontractions. These algorithms were already studied in [G.L. Acedo, H.-K. Xu] and [N. Nadezhkina, W. Takahashi] but our aim here is to provide the links between these know algorithms and the general framework of ${\cal T}$-class algorithms studied in [H.H. Bauschke, P.L. Combettes].

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