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A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization. (English) Zbl 1198.47082
From the summary: We introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. As applications, at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings.
MSC:
47J25Iterative procedures (nonlinear operator equations)
47J20Inequalities involving nonlinear operators
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces