Strong convergence theorem on split equilibrium and fixed point problems in Hilbert spaces. (English) Zbl 1427.47025
The authors prove that any sequence generated by an iterative algorithm converges strongly to some point which is a common solution of split equilibrium, variational inequality and fixed point problems for asymptotically nonexpansive mappings in Hilbert spaces. The main result extends the corresponding result for nonexpansive mappings due to K. R. Kazmi and S. H. Rizvi [J. Egypt. Math. Soc. 21, No. 1, 44–51 (2013: Zbl 1277.49009)].
Reviewer: In-Sook Kim (Suwon)
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 49J40 | Variational inequalities |
| 47H10 | Fixed-point theorems |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
split equilibrium problem; nonexpansive mappings; split feasible solution; Hilbert spaces; variational inequality; nonexpansive mappings; iterative algorithm; strong convergenceCitations:
Zbl 1277.49009References:
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