Krasnosel’skiǐ–Mann-Type Subgradient Extragradient Algorithms for Variational Inequality and Hierarchical Fixed-Point Problems

Monairah Alansari, Rehan Ali and Mohammad Farid ()
Additional contact information
Monairah Alansari: Department of Mathematics, King Abdulaziz University, Jeddah 22254, Saudi Arabia
Rehan Ali: Department of Mathematics, Central University of Kashmir, Ganderbal 191131, Jammu and Kashmir, India
Mohammad Farid: Department of Mathematics, College of Science, Qassim University, Saudi Arabia

Mathematics, 2025, vol. 13, issue 23, 1-21

Abstract: In this work, we present a Krasnosel’skiǐ–Mann-type subgradient extragradient algorithm to solve variational inequalities and hierarchical fixed-point problems for nonexpansive and quasi-nonexpansive mappings in Hilbert spaces. We establish weak convergence of the generated sequences to a common solution and derive several related results. The algorithm is validated through numerical examples, and several applications are discussed to demonstrate the method’s applicability. The proposed approach extends and unifies existing methods and findings in this field.

Keywords: hierarchical fixed-point problem; iterative methods; variational inequality; Krasnosel’skiǐ–Mann-type subgradient extragradient; quasi-nonexpansive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/23/3740/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/23/3740/ (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:13:y:2025:i:23:p:3740-:d:1800020

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 ().