Convergence analysis for fixed point problem of asymptotically nonexpansive mappings and variational inequality problem in Hilbert spaces. (English) Zbl 1486.47117
Summary: The purpose of this paper is to study a new viscosity iterative algorithm for finding a common element of the set of fixed points of an asymptotically nonexpansive mapping and the set of solutions of a new variational inequality problem involving inverse-strongly monotone operators in Hilbert spaces. We prove some strong convergence theorems under some suitable assumptions imposed on the parameters by using a modified extragradient method. The results obtained in this paper may be an improvement of many recent ones in this fields.
MSC:
| 47J26 | Fixed-point iterations |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H10 | Fixed-point theorems |
Keywords:
modified extragradient method; strong convergence; variational inequality; fixed point; asymptotically nonexpansive mapping; Hilbert spacesReferences:
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