Construction of a common fixed point of firmly nonexpansive mappings. (Construction d’un point fixe commun à une famille de constractions fermes.) (French. Abridged English version) Zbl 0830.65047

Summary: We propose a general method for finding a common fixed point of countably many firmly nonexpansive mappings on a real Hilbert space and prove its convergence. In this method, the mappings are processed in variable blocks and the range of the relaxation parameters depends on the block chosen at each iteration.


65J15 Numerical solutions to equations with nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems