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

Censor, Yair; Segal, Alexander

J. Convex Anal. 16, No. 2, 587-600 (2009).

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.

Reviewer: Vasilis Dimitriou (Chania)

MSC:

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

Keywords:

Split common fixed point problem; parallel algorithm; convergence