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Open AccessArticle

Inertial Method for Bilevel Variational Inequality Problems with Fixed Point and Minimizer Point Constraints

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KMUTTFixed Point Research Laboratory, SCL 802 Fixed Point Laboratory & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
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Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, P.O. Box 445, Debre Berhan, Ethiopia
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Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
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Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(9), 841; https://doi.org/10.3390/math7090841
Received: 5 August 2019 / Revised: 30 August 2019 / Accepted: 2 September 2019 / Published: 11 September 2019
In this paper, we introduce an iterative scheme with inertial effect using Mann iterative scheme and gradient-projection for solving the bilevel variational inequality problem over the intersection of the set of common fixed points of a finite number of nonexpansive mappings and the set of solution points of the constrained optimization problem. Under some mild conditions we obtain strong convergence of the proposed algorithm. Two examples of the proposed bilevel variational inequality problem are also shown through numerical results. View Full-Text
Keywords: minimization problem; fixed point problem; inertial term; bilevel variational inequality minimization problem; fixed point problem; inertial term; bilevel variational inequality
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Yimer, S.E.; Kumam, P.; Gebrie, A.G.; Wangkeeree, R. Inertial Method for Bilevel Variational Inequality Problems with Fixed Point and Minimizer Point Constraints. Mathematics 2019, 7, 841.

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