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An iterative method for solving a system of mixed equilibrium problems, system of quasivariational inclusions, and fixed point problems of nonexpansive semigroups with application to optimization problems. (English) Zbl 1235.65074

Summary: We introduce a general implicit iterative scheme base on viscosity approximation method with a \(\varphi\)-strongly pseudocontractive mapping for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed point for a nonexpansive semigroup, and the set of solutions of system of variational inclusions with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator.

MSC:

65K15 Numerical methods for variational inequalities and related problems
49J40 Variational inequalities
65K10 Numerical optimization and variational techniques
47H10 Fixed-point theorems
65J99 Numerical analysis in abstract spaces
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