Modified Mann-Type Subgradient Extragradient Rules for Variational Inequalities and Common Fixed Points Implicating Countably Many Nonexpansive Operators

Yun-Ling Cui, Lu-Chuan Ceng, Fang-Fei Zhang, Cong-Shan Wang, Jian-Ye Li, Hui-Ying Hu and Long He
Additional contact information
Yun-Ling Cui: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Lu-Chuan Ceng: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Fang-Fei Zhang: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Cong-Shan Wang: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Jian-Ye Li: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Hui-Ying Hu: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Long He: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Mathematics, 2022, vol. 10, issue 11, 1-26

Abstract: In a real Hilbert space, let the CFPP, VIP, and HFPP denote the common fixed-point problem of countable nonexpansive operators and asymptotically nonexpansive operator, variational inequality problem, and hierarchical fixed point problem, respectively. With the help of the Mann iteration method, a subgradient extragradient approach with a linear-search process, and a hybrid deepest-descent technique, we construct two modified Mann-type subgradient extragradient rules with a linear-search process for finding a common solution of the CFPP and VIP. Under suitable assumptions, we demonstrate the strong convergence of the suggested rules to a common solution of the CFPP and VIP, which is only a solution of a certain HFPP.

Keywords: modified Mann-type subgradient extragradient rule; linear-search process; variational inequality problem; countable nonexpansive operators; strong convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/11/1949/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/11/1949/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:11:p:1949-:d:832736

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().