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Iterative methods for generalized split feasibility problems in Hilbert spaces. (English) Zbl 1326.47099

Summary: Generalized split feasibility problems governed by generalized hybrid mappings are studied via iterative methods. Several algorithms are introduced to solve them. In particular, weak convergence of these algorithms is proved. As tools, averaged mappings and resolvents of maximal monotone operators are technically manoeuvered to facilitate the argument of the proofs to the main results. Applications to Mann’s iteration method for nonexpansive mappings and to equilibrium problems are included.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H05 Monotone operators and generalizations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H20 Semigroups of nonlinear operators
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