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The split common fixed point problem for directed operators. (English) Zbl 1189.65111
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.

MSC:
65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
65Y05Parallel computation (numerical methods)