Fejér Monotonicity and Fixed Point Iterations
A sequence is Fejér monotone with respect to a set C if each point in the sequence is not strictly farther from any point in C than its predecessor. Such sequences possess very attractive properties that greatly 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 nonexpansive operators.
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