Strong convergence of the viscosity approximation method for the split generalized equilibrium problem. (English) Zbl 07501022
Summary: In this paper, we consider a common solution of three problems in real Hilbert spaces including the split generalized equilibrium problem, the variational inequality problem and the fixed point problem for nonexpansive multivalued mappings. For finding the solution, we present a modified viscosity approximation method and prove a strong convergence theorem under mild conditions. Moreover, we also provide a numerical example to illustrate the convergence behavior of the proposed iterative method.
MSC:
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H10 | Fixed-point theorems |
Keywords:
split generalized equilibrium problems; variational inequality problems; viscosity approximation method; nonexpansive multivalued mappings; Hilbert spacesReferences:
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