Viscosity iterative scheme for generalized mixed equilibrium problems and nonexpansive semigroups

Mohammad Eslamian ^[1] ; Ali Abkar ^[2]
1. [1] Islamic Azad University
  
  Islamic Azad University
  
  Irán
2. [2] Imam Khomeini International University
  
  Imam Khomeini International University
  
  Irán
Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 22, Nº. 2, 2014, págs. 554-570
Idioma: inglés
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Resumen
- 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.