Viscosity iterative process for demicontractive mappings and multivalued mappings and equilibrium problems

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...

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Bibliographic Details
Published in:Computational & applied mathematics 2017-09, Vol.36 (3), p.1239-1253
Main Authors: Eslamian, M., Saadati, R., Vahidi, J.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Mapping
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Optimization
Viscosity
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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.
ISSN:0101-8205
2238-3603
1807-0302
DOI:10.1007/s40314-015-0292-6