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A viscosity approximation scheme for finding common solutions of mixed equilibrium problems, a finite family of variational inclusions, and fixed point problems in Hilbert spaces. (English) Zbl 1245.49019
Summary: We introduce an iterative method for finding a common element of set of fixed-points of nonexpansive mappings, the set of solutions of a finite family of variational inclusion with set-valued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of a mixed equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper improve and extend the main results of Plubtemg and Sripard and many others.

MSC:
49J45 Methods involving semicontinuity and convergence; relaxation
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25 Iterative procedures involving nonlinear operators
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