Inertial subgradient extragradient with projection method for solving variational inequality and fixed point problems

Abstract

In this paper, we introduce a new modified inertial Mann-type method that combines the subgradient extragradient method with the projection contraction method for solving quasimonotone variational inequality problems and fixed point problems in real Hilbert spaces. We establish strong convergence of the proposed method under some mild conditions without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of the method over the existing one in the literature.

Keywords

• fixed point
• quasimonotone operator
• variational inequality problem
• demimetric mapping
• strong convergence