Abstract
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.
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References
H. S. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal., 57 (2004), pp. 35–61.
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Bauschke, H.H., Combettes, P.L. (2017). Fejér Monotonicity and Fixed Point Iterations. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-48311-5_5
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DOI: https://doi.org/10.1007/978-3-319-48311-5_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48310-8
Online ISBN: 978-3-319-48311-5
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