Fixed Point Theory and Applications
Volume 2004 (2004), Issue 2, Pages 135-147

Quadratic optimization of fixed points for a family of nonexpansive mappings in Hilbert space

B. E. Rhoades

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.


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.