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Hybrid proximal-type algorithms for generalized equilibrium problems, maximal monotone operators, and relatively nonexpansive mappings. (English) Zbl 1214.47078
Summary: The purpose of this paper is to introduce and consider new hybrid proximal-type algorithms for finding a common element of the set EP of solutions of a generalized equilibrium problem, the set F(S) of fixed points of a relatively nonexpansive mapping S, and the set T -1 0 of zeros of a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space. Strong convergence theorems for these hybrid proximal-type algorithms are established; that is, under appropriate conditions, the sequences generated by these various algorithms converge strongly to the same point in EPF(S)T -1 0. These new results represent the improvement, generalization, and development of the previously known ones in the literature.
MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
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