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A relaxed hybrid steepest descent method for common solutions of generalized mixed equilibrium problems and fixed point problems. (English) Zbl 1315.47071

Summary: In the setting of Hilbert spaces, we introduce a relaxed hybrid steepest descent method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of a variational inequality for an inverse strongly monotone mapping and the set of solutions of generalized mixed equilibrium problems. We prove the strong convergence of the method to the unique solution of a suitable variational inequality. The results obtained in this article improve and extend the corresponding results.

MSC:

47J25 Iterative procedures involving nonlinear operators
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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