Viscosity extragradient algorithms with double inertial extrapolation steps for quasimonotone variational inequalities and fixed point problems

Abstract

We study two viscosity extragradient algorithms with double inertial extrapolation steps for finding a common solution of a variational inequality governed by a quasimonotone operator and of a fixed point problem with a demicontractive mapping in a real Hilbert space. The strong convergence theorems are proved under certain appropriate conditions. The step sizes of our algorithms are updated by simple calculations without knowing the prior information of the operator norms. Numerical examples in finite- and infinite-dimensional spaces are given to show the performance of the proposed algorithms.

Keywords:

• Inertial
• quasimonotone mapping
• subgradient extragradient
• variational inequality
• fixed point

2020 Mathematics Subject Classifications:

• 47J25
• 47J20
• 49J40
• 47H09

Acknowledgments

The authors were indebted to the anonymous referees for their helpful comments and suggestions which improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).