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On Strengthened Inertial-Type Subgradient Extragradient Rule with Adaptive Step Sizes for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive Mappings.
- Source :
- Mathematics (2227-7390); Mar2022, Vol. 10 Issue 6, p958, 21p
- Publication Year :
- 2022
-
Abstract
- In a real Hilbert space, let the VIP denote a pseudomonotone variational inequality problem with Lipschitz continuity operator, and let the CFPP indicate a common fixed-point problem of finitely many nonexpansive mappings and an asymptotically nonexpansive mapping. On the basis of the Mann iteration method, the viscosity approximation method and the hybrid steepest-descent method, we propose and analyze two strengthened inertial-type subgradient extragradient rules with adaptive step sizes for solving the VIP and CFPP. With the help of suitable restrictions, we show the strong convergence of the suggested rules to a common solution of the VIP and CFPP, which is the unique solution of a hierarchical variational inequality (HVI). [ABSTRACT FROM AUTHOR]
- Subjects :
- NONEXPANSIVE mappings
HILBERT space
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 10
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 156071977
- Full Text :
- https://doi.org/10.3390/math10060958