Abstract
Given a finite family of nonexpansive self-mappings of a Hilbert
space, a particular quadratic functional, and a strongly positive
selfadjoint bounded linear operator, Yamada et al. defined
an iteration scheme which converges to the unique minimizer of the
quadratic functional over the common fixed point set of the
mappings. In order to obtain their result, they needed to assume
that the maps satisfy a commutative type condition. In this paper,
we establish their conclusion without the assumption of any type
of commutativity.