Viscosity-type inertial iterative methods for variational inclusion and fixed point problems

Abstract

In this paper, we have introduced some viscosity-type inertial iterative methods for solving fixed point and variational inclusion problems in Hilbert spaces. Our methods calculated the viscosity approximation, fixed point iteration, and inertial extrapolation jointly in the starting of every iteration. Assuming some suitable assumptions, we demonstrated the strong convergence theorems without computing the resolvent of the associated monotone operators. We used some numerical examples to illustrate the efficiency of our iterative approaches and compared them with the related work.

Keywords

• viscosity method
• inertial extrapolation
• fixed point problem
• variational inclusion
• strong convergence