Fejér Monotonicity and Fixed Point Iterations
Heinz H. Bauschke, Patrick L. Combettes · CMS books in mathematics · 2017
A sequence is Fejér monotone with respect to a set C if no point of the sequence is strictly farther from any point in C than its predecessor. Such sequences possess attractive properties that simplify the analysis of their asymptotic behavior. In this chapter, we provide the basic theory for Fejér monotone sequences and apply it to obtain in a systematic fashion convergence results for various classical iterations involving (quasi)nonexpansive operators.