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

Autor:	Lu-Chuan Ceng, Adrian Petruşel, Jen-Chih Yao
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	method with line-search process pseudomonotone variational inequality strictly pseudocontractive mappings common fixed point sequentially weak continuity Mathematics QA1-939
Zdroj:	Mathematics, Vol 7, Iss 10, p 925 (2019)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math7100925
Popis:	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).
Databáze:	Directory of Open Access Journals
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