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Shrinking projection methods for firmly nonexpansive mappings. (English) Zbl 1238.47043
Summary: We study the shrinking projection method for firmly nonexpansive mappings. The method gives us a strong convergence iteration for a family of firmly nonexpansive mappings and also permit us to obtain a sufficient condition for the existence of a fixed point of a firmly nonexpansive mapping.

MSC:
 47J25 Iterative procedures involving nonlinear operators 47H05 Monotone operators and generalizations 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems
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References:
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