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Zbl 1189.65111
Censor, Yair; Segal, Alexander
The split common fixed point problem for directed operators. (English)
[J] J. Convex Anal. 16, No. 2, 587-600 (2009). ISSN 0944-6532

The split common fixed point problem (SCFPP) that requires the finding of a common fixed point of a family of operators in one space, whose image, under a linear transformation, is a common fixed point of another family of operators in the image space, is proposed. A parallel algorithm for the solution of this SCFPP problem for the class of directed operators is further formulated and analyzed. The convergence of the algorithm is proved and a way it unifies and generalizes previously discussed problems and algorithms is noted.
[Vasilis Dimitriou (Chania)]

MSC 2000:: *65J15 Equations with nonlinear operators (numerical methods)
47J25 Methods for solving nonlinear operator equations (general)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
65Y05 Parallel computation (numerical methods)

Keywords: Split common fixed point problem; parallel algorithm; convergence

Cited in: Zbl 1232.49017 Zbl 1219.90185

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