Fixed points of averages of resolvents: geometry and algorithms (Q2902868)

This gorgeously written paper is devoted to generalizing the article of \textit{X.-F. Wang} and \textit{H. H. Bauschke} [Nonlinear Anal. Theory Methods Appl. 74, No. 13, 4550--4572 (2011; Zbl 1228.47052)] for general cases. The authors provide a correspondence between a set of fixed points of averaged resolvents and an effectively defined set described in a product space, which is the fixed point set of compositions of averaged operators. Furthermore, a novel algorithm for finding the fixed point of the resolvent is also presented. Akin to the Gauss-Seidel iteration that can be viewed as a modification of the Jacobi iteration, they establish a new iteration procedure and, moreover, give an example of an inconsistent linear system of equations.