Fixed Point Theory and Applications
Volume 2004 (2004), Issue 2, Pages 135-147
doi:10.1155/S1687182004309046
Quadratic optimization of fixed points for a family of nonexpansive mappings in Hilbert space
Department of Mathematics, Indiana University, Bloomington 47405-7106, IN, USA
Received 10 September 2003
Copyright © 2004 B. E. Rhoades. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.