On Mann Viscosity Subgradient Extragradient Algorithms for Fixed Point Problems of Finitely Many Strict Pseudocontractions and Variational Inequalities

Lu-Chuan Ceng, Adrian Petruşel 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 Babeş-Bolyai University, Cluj-Napoca 400084, Romania
Jen-Chih Yao: Research Center for Interneural Computing, China Medical University Hospital, Taichung 40447, Taiwan

Mathematics, 2019, vol. 7, issue 10, 1-14

Abstract: In a real Hilbert space, we denote CFPP and VIP as common fixed point problem of finitely many strict pseudocontractions and a variational inequality problem for Lipschitzian, pseudomonotone operator, respectively. This paper is devoted to explore how to find a common solution of the CFPP and VIP. To this end, we propose Mann viscosity algorithms with line-search process by virtue of subgradient extragradient techniques. The designed algorithms fully assimilate Mann approximation approach, viscosity iteration algorithm and inertial subgradient extragradient technique with line-search process. Under suitable assumptions, it is proven that the sequences generated by the designed algorithms converge strongly to a common solution of the CFPP and VIP, which is the unique solution to a hierarchical variational inequality (HVI).

Keywords: method with line-search process; pseudomonotone variational inequality; strictly pseudocontractive mappings; common fixed point; sequentially weak continuity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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