Quadratic optimization of fixed points for a family of nonexpansive mappings in Hilbert space
Fixed Point Theory and Applications volume 2004, Article number: 169756 (2004)
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.
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Rhoades, B. Quadratic optimization of fixed points for a family of nonexpansive mappings in Hilbert space. Fixed Point Theory Appl 2004, 169756 (2004). https://doi.org/10.1155/S1687182004309046