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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:

65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
65Y05 Parallel numerical computation
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