Algorithms of common solutions for a variational inequality, a split equilibrium problem and a hierarchical fixed point problem. (English) Zbl 1296.49006
Summary: In this paper, we suggest and analyze an iterative scheme for finding an approximate element of the common set of solutions of a split equilibrium problem, a variational inequality problem and a hierarchical fixed-point problem in a real Hilbert space. We also consider the strong convergence of the proposed method under some conditions. The results proved in this paper may be viewed as an improvement and refinement of the previously known results.
MSC:
| 49J40 | Variational inequalities |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H10 | Fixed-point theorems |
Keywords:
split equilibrium problem; variational inequality problem; hierarchical fixed-point problem; projection method; strictly pseudo-contractive mappingReferences:
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