An extragradient iterative scheme for common fixed point problems and variational inequality problems with applications

Abstract

In this paper, by combining a modified extragradient scheme with the viscosity approximation technique, an iterative scheme is developed for computing the common element of the set of fixed points of a sequence of asymptotically nonexpansive mappings and the set of solutions of the variational inequality problem for an α-inverse strongly monotone mapping. We prove a strong convergence theorem for the sequences generated by this scheme and give some applications of our convergence theorem.

Keywords

• modified extragradient method
• viscosity approximation method
• α-inverse strongly monotone mapping
• sequence of asymptotically nonexpansive mappings
• variational inequalities
• af point property
• primary 47h10
• secondary 54h25