Inertial projection methods for solving general quasi-variational inequalities

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 alter...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 2; pp. 1075 - 1086
Main Authors Jabeen, Saudia, B. Mohsen, Bandar, Aslam Noor, Muhammad, Inayat Noor, Khalida
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
convergence
inertial methods
inertial term
projection operator
quasi-variational inequality
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021064

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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021064