The hybrid projection methods for pseudocontractive, nonexpansive semigroup, and monotone mapping. (English) Zbl 1473.47036
Summary: We modify the three-step iterative schemes to prove the strong convergence theorems by using the hybrid projection methods for finding a common element of the set of solutions of fixed points for a pseudocontractive mapping and a nonexpansive semigroup mapping and the set of solutions of a variational inequality problem for a monotone mapping in a Hilbert space under some appropriate control conditions. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H20 | Semigroups of nonlinear operators |
| 47H05 | Monotone operators and generalizations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
three-step iterative schemes; strong convergence; hybrid projection methods; pseudocontractive mapping; nonexpansive semigroup; Hilbert spaceReferences:
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