Iterative algorithm for a family of split equilibrium problems and fixed point problems in Hilbert spaces with applications. (English) Zbl 1346.47068
Summary: In this paper, we propose an iterative algorithm and, by using the proposed algorithm, prove some strong convergence theorems for finding a common element of the set of solutions of a finite family of split equilibrium problems and the set of common fixed points of a countable family of nonexpansive mappings in Hilbert spaces. An example is given to illustrate the main result of this paper. As an application, we construct an algorithm to solve an optimization problem.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 90C30 | Nonlinear programming |
Keywords:
split equilibrium problem; nonexpansive mapping; split feasible solution problem; Hilbert spaceReferences:
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