Solving Hierarchical Variational Inequality for Almost Mean Nonexpansive Mappings

Noor Saddam Taresh, Department of Mathematics, College of Education, Ibn Al-Haitham, University of Baghdad, Baghdad, IraqFollow
Salwa Salman Abed, Department of Mathematics, College of Education, Ibn Al-Haitham, University of Baghdad, Baghdad, IraqFollow

Abstract

A clear common method in solving some types of nonlinear problems is to exchange the original problem with a collection of regularized problems and all these regularized problems have exactly one solution. A particular solution of the original problem will be obtained as a limit of these unique solutions of the regularized problems. This idea is used to provide a method for the hierarchical fixed point approach to solving variational inequality problems (VIPs). In this work, we intend to study two new iterative schemes by examining their strong convergence to a common fixed point for mappings defined for a nonempty closed and convex D subset of a real Hilbert space Ξ. These iterative schemes are constructed for sequences of almost mean nonexpansive mappings and nonexpansive mappings under some control conditions. Firstly, strong convergence results are established for two iterative schemes for three mappings: the first Γ : D⟶Ξ is a contraction mapping, the second P_n : D ⟶ Ξ is a sequence of nonexpansive mappings, and the third K_n : D ⟶ D is a sequence of almost mean nonexpansive mappings. Secondly, when the constraints on parameters of two iterative schemes are relaxed, this yields other strong convergence results which also are solutions of hierarchical fixed point problem (HFPP). Finally, a solution of the quadratic minimization problem is found as a special case and this convergence is unique. Our results contain the former studies as particular statuses, and can be seen as a rededication and amelioration of many corresponding familiar results of hierarchical variational inequality problems (HVIP)

Keywords

Contraction Mapping, Hierarchical Variational Inequality, Real Hilbert Space, Sequence of Nonexpansive Mappings, Strong Convergence

Subject Area

Mathematics

Article Type

Article

First Page

2321

Last Page

2339

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite this Article

Taresh, Noor Saddam and Abed, Salwa Salman (2025) "Solving Hierarchical Variational Inequality for Almost Mean Nonexpansive Mappings," Baghdad Science Journal: Vol. 22: Iss. 7, Article 19.
DOI: https://doi.org/10.21123/2411-7986.4999

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