Abstract
In this paper, we propose a new general iterative scheme based on the viscosity approximation method for finding a common element of the set of solutions of the generalized mixed equilibrium problem and the set of all common fixed points of a finite family of nonexpansive semigroups. Then, we prove the strong convergence of the iterative scheme to find a unique solution of the variational inequality that is the optimality condition for the minimization problem. Our results extend and improve some recent results of Cianciaruso et al. (J. Optim. Theory Appl. 146:491–509, 2010), Kamraksa and Wangkeeree (J. Glob. Optim. 51:689–714, 2011), and many others.
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Acknowledgements
Research of the second author was supported in part by a grant no. 751164-1392 from Imam Khomeini International University.
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Eslamian, M., Abkar, A. Viscosity iterative scheme for generalized mixed equilibrium problems and nonexpansive semigroups. TOP 22, 554–570 (2014). https://doi.org/10.1007/s11750-012-0270-8
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DOI: https://doi.org/10.1007/s11750-012-0270-8
Keywords
- Nonexpansive semigroup
- Generalized mixed equilibrium problem
- Fixed point
- Viscosity approximation method