Strong convergence of an iterative method for variational inequality problems and fixed point problems

Xiaolong Qin1, Shin Min Kang1, Yongfu Su2, and Meijuan Shang3

1 Department of Mathematics and the RINS Gyeongsang National University Jinju 660-701, Korea (S.M. Kang)
2 Department of Mathematics Tianjin Polytechnic University Tianjin 300160, China
3 Department of Mathematics Shijiazhuang University Shijiazhuang 050035, China


Abstract: In this paper, we introduce a general iterative scheme to investigate the problem of finding a common element of the fixed point set of a strict pseudocontraction and the solution set of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Strong convergence theorems are established in a real Hilbert space.

AMSclassification: primary 47H09; secondary 47J25.

Keywords: nonexpansive mapping, strict pseudocontraction, fixed point, variational inequality, relaxed cocoercive mapping.