Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings. (English) Zbl 1228.47061
Summary: We introduce an iterative sequence for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping and the set of solutions of a variational inequality in a Banach space. Our results extend and improve the recent ones announced by J.-L. Li [J. Math. Anal. Appl. 295, No. 1, 115–126 (2004; Zbl 1045.49008)], J.-H. Fan [J. Math. Anal. Appl. 337, No. 2, 1041–1047 (2008; Zbl 1140.49011)], and many others.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H05 | Monotone operators and generalizations |
| 47J05 | Equations involving nonlinear operators (general) |
Keywords:
iterative sequence; fixed points; relatively weak nonexpansive mapping; variational inequality; Banach spaceReferences:
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