Best approximation mappings in Hilbert spaces

The notion of best approximation mapping (BAM) with respect to a closed affine subspace in finite-dimensional spaces was introduced by Behling, Bello Cruz and Santos show the linear convergence block-wise circumcentered-reflection method. possesses two critical properties circumcenter for convergence. Because iteration sequence BAM linearly converges, is interesting its own right. In this paper, we naturally extend definition from subspaces nonempty convex sets $${\mathbb {R}}^{n}$$ general Hilbert spaces. We discover that set associated must be fixed point BAM. Hence, generated converges nearest Connections between BAMs other mappings generating convergent sequences are considered. Behling et al. proved finite composition still . generalize their result also construct new constant BAMs. This provides proof method alternating projections. Moreover, compositions investigated. addition, combinations Last but not least, connect report on Cegielski’s results relationships strongly quasinonexpansive mappings.