Convergence analysis for fixed point problem of asymptotically nonexpansive mappings and variational inequality problem in Hilbert spaces. (3rd June 2021) - Dong, Qiao-Li; Cai, Gang
Abstract : 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.