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Strong convergence of an iterative algorithm for hierarchical problems. (English) Zbl 1473.47038

Summary: We introduce the triple hierarchical problem over the solution set of the variational inequality problem and the fixed point set of a nonexpansive mapping. The strong convergence of the algorithm is proved under some mild conditions. Our results extend those of Y.-H. Yao et al. [J. Appl. Math. Comput. 31, No. 1–2, 433–445 (2009; Zbl 1223.47106); Fixed Point Theory Appl. 2011, Article ID 794203, 12 p. (2011; Zbl 1215.49020)], H. Iiduka [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e1292–e1297 (2009; Zbl 1238.65061)], L.-C. Ceng et al. [J. Optim. Theory Appl. 151, No. 3, 489–512 (2011; Zbl 1262.90175)], and other authors.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
49J40 Variational inequalities

References:

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