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A new hybrid algorithm for variational inclusions, generalized equilibrium problems, and a finite family of quasi-nonexpansive mappings. (English) Zbl 1186.47060
Summary: We propose a new iterative scheme for finding common elements of the set of fixed points of a finite family of quasi-nonexpansive mappings, the set of solutions of variational inclusions, and the set of solutions of generalized equilibrium problems. Some strong convergence results are derived by using the concept of $W$-mappings for a finite family of quasi-nonexpansive mappings under suitable conditions in Hilbert spaces.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47J22Variational and other types of inclusions
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