Inertial-Like Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive and Strictly Pseudocontractive Mappings

Lu-Chuan Ceng, Adrian Petruşel, Ching-Feng Wen and Jen-Chih Yao
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Lu-Chuan Ceng: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Adrian Petruşel: Department of Mathematics, Babes-Bolyai University, Cluj-Napoca 400084, Romania
Ching-Feng Wen: Center for Fundamental Science and Research Center for Nonliear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
Jen-Chih Yao: Research Center for Interneural Computing, China Medical University Hospital, Taichung 40402, Taiwan

Mathematics, 2019, vol. 7, issue 9, 1-19

Abstract: Let VIP indicate the variational inequality problem with Lipschitzian and pseudomonotone operator and let CFPP denote the common fixed-point problem of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping in a real Hilbert space. Our object in this article is to establish strong convergence results for solving the VIP and CFPP by utilizing an inertial-like gradient-like extragradient method with line-search process. Via suitable assumptions, it is shown that the sequences generated by such a method converge strongly to a common solution of the VIP and CFPP, which also solves a hierarchical variational inequality (HVI).

Keywords: inertial-like subgradient-like extragradient method with line-search process; pseudomonotone variational inequality problem; asymptotically nonexpansive mapping; strictly pseudocontractive mapping; sequentially weak continuity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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