Inertial projection methods for solving general quasi-variational inequalities

Saudia Jabeen; Bandar Bin-Mohsin; Muhammad Aslam Noor; Khalida Inayat Noor; Saudia Jabeen; Bandar Bin-Mohsin; Muhammad Aslam Noor; Khalida Inayat Noor

doi:10.3934/math.2021064

AIMS Mathematics

2021, Volume 6, Issue 2: 1075-1086. doi: 10.3934/math.2021064

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Research article

Inertial projection methods for solving general quasi-variational inequalities

1.
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
2.
Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia

Received: 24 July 2020 Accepted: 02 November 2020 Published: 09 November 2020
MSC : 49J40, 90C33

In this paper, we consider a new class of quasi-variational inequalities, which is called the general quasi-variational inequality. Using the projection operator technique, we establish the equivalence between the general quasi-variational inequalities and the fixed point problems. We use this alternate formulation to propose some new inertial iterative schemes for solving the general quasi-variational inequalities. The convergence criteria of the new inertial projection methods under some appropriate conditions is investigated. Since the general quasi-variational inequalities include the quasi-variational inequalities, variational inequalities, complementarity problems and the related optimization problems as special cases, our results continue to hold for these problems. It is an interesting problem to compare the efficiency of the proposed methods with other known methods.
- quasi-variational inequality,
- inertial term,
- projection operator,
- inertial methods,
- convergence
Citation: Saudia Jabeen, Bandar Bin-Mohsin, Muhammad Aslam Noor, Khalida Inayat Noor. Inertial projection methods for solving general quasi-variational inequalities[J]. AIMS Mathematics, 2021, 6(2): 1075-1086. doi: 10.3934/math.2021064

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Abstract

In this paper, we consider a new class of quasi-variational inequalities, which is called the general quasi-variational inequality. Using the projection operator technique, we establish the equivalence between the general quasi-variational inequalities and the fixed point problems. We use this alternate formulation to propose some new inertial iterative schemes for solving the general quasi-variational inequalities. The convergence criteria of the new inertial projection methods under some appropriate conditions is investigated. Since the general quasi-variational inequalities include the quasi-variational inequalities, variational inequalities, complementarity problems and the related optimization problems as special cases, our results continue to hold for these problems. It is an interesting problem to compare the efficiency of the proposed methods with other known methods.

References

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