On Mann-Type Subgradient-like Extragradient Method with Linear-Search Process for Hierarchical Variational Inequalities for Asymptotically Nonexpansive Mappings

Lu-Chuan Ceng, Jen-Chih Yao and Yekini Shehu
Additional contact information
Lu-Chuan Ceng: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Jen-Chih Yao: Research Center for Interneural Computing, China Medical University, Taichung 40402, Taiwan
Yekini Shehu: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Mathematics, 2021, vol. 9, issue 24, 1-17

Abstract: We propose two Mann-type subgradient-like extra gradient iterations with the line-search procedure for hierarchical variational inequality (HVI) with the common fixed-point problem (CFPP) constraint of finite family of nonexpansive mappings and an asymptotically nonexpansive mapping in a real Hilbert space. Our methods include combinations of the Mann iteration method, subgradient extra gradient method with the line-search process, and viscosity approximation method. Under suitable assumptions, we obtain the strong convergence results of sequence of iterates generated by our methods for a solution to HVI with the CFPP constraint.

Keywords: Mann-type subgradient-like extragradient method with line-search process; hierarchical variational inequality; common fixed point problem; asymptotically nonexpansive mapping; L continuity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/24/3322/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/24/3322/ (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:9:y:2021:i:24:p:3322-:d:706572

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 ().