Strong convergence of perturbed Mann iteration for systems of variational inequality problems over the set of common fixed points of a finite family of demicontractive mappings in Banach spaces
Volume 17, Issue 1, pp 70--81
https://dx.doi.org/10.22436/jnsa.017.01.04
Publication Date: February 14, 2024
Submission Date: October 27, 2023
Revision Date: December 01, 2023
Accteptance Date: December 05, 2023
Authors
T. M. M. Sow
- Universite Amadou Mahtar Mbow, Senegal.
Abstract
In this paper, we propose an iterative algorithm, which is based on the Mann iterative method for solving simultaneously common fixed point problem with a finite family of demicontractive mappings and systems of variational inequalities involving an infinite family of strongly accretive operators. Under suitable assumptions, we prove the strong convergence of this algorithm in Banach spaces. Application to systems of constrained convex minimization problem is provided to support our main results. The results of this paper improve and extend results of [M. Eslamian, C. R. Math. Acad. Sci. Paris, \(\bf 355\) (2017), 1168--1177], and of many others.
Share and Cite
ISRP Style
T. M. M. Sow, Strong convergence of perturbed Mann iteration for systems of variational inequality problems over the set of common fixed points of a finite family of demicontractive mappings in Banach spaces, Journal of Nonlinear Sciences and Applications, 17 (2024), no. 1, 70--81
AMA Style
Sow T. M. M., Strong convergence of perturbed Mann iteration for systems of variational inequality problems over the set of common fixed points of a finite family of demicontractive mappings in Banach spaces. J. Nonlinear Sci. Appl. (2024); 17(1):70--81
Chicago/Turabian Style
Sow, T. M. M.. "Strong convergence of perturbed Mann iteration for systems of variational inequality problems over the set of common fixed points of a finite family of demicontractive mappings in Banach spaces." Journal of Nonlinear Sciences and Applications, 17, no. 1 (2024): 70--81
Keywords
- Perturbed Mann iteration
- systems of variational inequalities
- demicontractive operators
- strongly accretive operators
MSC
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