A Hierarchical Presentation of Operators with Fixed Points on Hilbert Spaces
G. Crombez · Numerical Functional Analysis and Optimization · 2006
For problems that are aimed at obtaining a common fixed point of a countable class (T i ) i∈I of operators by an iterative procedure, usually an important role is played by an inequality that expresses the behavior of the distances of the original points x and their images T i x to the common fixed point set. The different inequalities that have appeared in the literature seem to impose a classification of the operators in two types; we propose a hierarchical description of the classes belonging to each type, based on some non-negative parameter. This hierarchical presentation makes it easier to investigate (existing or new) results concerning iterative procedures with respect to the possibility of broadening their scope of applicability.