Strong convergence of the composite Halpern iteration. (English) Zbl 1135.47052

A three-step fixed point iteration procedure of Halpern type is used to approximate fixed points of nonexpansive mappings in uniformly smooth Banach spaces. A strong convergence theorem is proved for this iteration procedure.


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
Full Text: DOI


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