Viscosity iterative process for demicontractive mappings and multivalued mappings and equilibrium problems. (English) Zbl 1370.47060
Summary: In this paper, we introduce a general iterative scheme based on the viscosity approximation method for finding a common element of the set of solutions of the equilibrium problem and the set of all fixed points of a demicontractive mapping and a generalized nonexpansive multivalued mapping. Then, we prove the strong convergence of the iterative scheme to find a unique solution of the variational inequality which is the optimality condition for the minimization problem. The main results presented in this paper extend various results existing in the current literature.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H04 | Set-valued operators |
Keywords:
demicontractive mapping; equilibrium problem; fixed point; generalized nonexpansive multivalued mapping; viscosity approximation method; strong convergenceReferences:
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