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Solving monotone inclusions via compositions of nonexpansive averaged operators. (English) Zbl 1153.47305
Summary: A unified fixed point theoretic framework is proposed to investigate the asymptotic behavior of algorithms for finding solutions to monotone inclusion problems. The basic iterative scheme under consideration involves nonstationary compositions of perturbed averaged nonexpansive operators. The analysis covers proximal methods for common zero problems as well as for various splitting methods for finding a zero of the sum of monotone operators.

MSC:
47H10 Fixed-point theorems
47H05 Monotone operators and generalizations
47N20 Applications of operator theory to differential and integral equations
54H25 Fixed-point and coincidence theorems (topological aspects)
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