A hybrid viscosity iterative method with averaged mappings for split equilibrium problems and fixed point problems. (English) Zbl 1382.47028
Summary: In this paper, with the help of averaged mappings, we introduce and study a hybrid iterative method to approximate a common solution of a split equilibrium problem and a fixed point problem of a finite collection of nonexpansive mappings. We prove that the sequences generated by the iterative scheme strongly converges to a common solution of the above problems. We give some numerical examples to ensure that our iterative scheme is more efficient than the methods of S. Plubtieng and R. Punpaeng [J. Math. Anal. Appl. 336, No. 1, 455–469 (2007; Zbl 1127.47053)], Y. Liu [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 10, 4852–4861 (2009; Zbl 1222.47104)] and D.-J. Wen and Y.-A. Chen [Fixed Point Theory Appl. 2012, Paper No. 125, 15 p. (2012; Zbl 1475.47080)].
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H10 | Fixed-point theorems |
| 49J40 | Variational inequalities |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
nonexpansive mapping; averaged mapping; split equilibrium problem; strong convergence; variational inequality problem; fixed point problem; hybrid iterative methodReferences:
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