Journal of Convex Analysis 16 (2009), No. 2, 587--600
Copyright Heldermann Verlag 2009
The Split Common Fixed Point Problem for Directed Operators
Yair Censor
Dept. of Mathematics, University of Haifa, Mt. Carmel, Haifa 31905, Israel
yair@math.haifa.ac.il
Alexander Segal
Dept. of Mathematics, University of Haifa, Mt. Carmel, Haifa 31905, Israel
asegal@math.haifa.ac.il
We propose the split common fixed point problem that requires to find 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. We formulate and analyze a parallel algorithm for solving this split common fixed point problem for the class of directed operators and note how it unifies and generalizes previously discussed problems and algorithms.
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