Inertial KM-type extragradient scheme for solving a variational inequality and a hierarchical fixed point problems

Abstract

Abstract We propose an inertial KM-type extragradient scheme to approximate a common solution of a variational inequality problem and a hierarchical fixed point problem for nonexpansive mappings. This scheme generalizes and unifies a number of known iterative schemes. Furthermore, we discuss the weak convergence for the proposed scheme. We also discuss an example to illustrate the main theorem.

Keywords

• Hierarchical fixed point problem
• Variational inequality
• Inertial KM-type scheme
• Nonexpansive mapping