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Volume 41, Issue 1
A Hybrid Viscosity Approximation Method for a Common Solution of a General System of Variational Inequalities, an Equilibrium Problem, and Fixed Point Problems

Maryam Yazdi & Saeed Hashemi Sababe

DOI: 10.4208/jcm.2106-m2020-0209

J. Comp. Math., 41 (2023), pp. 153-172.

Published online: 2022-11

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  • Abstract

In this paper, we introduce a new iterative method based on the hybrid viscosity approximation method for finding a common element of the set of solutions of a general system of variational inequalities, an equilibrium problem, and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert space. We prove a strong convergence theorem of the proposed iterative scheme under some suitable conditions on the parameters. Furthermore, we apply our main result for W-mappings. Finally, we give two numerical results to show the consistency and accuracy of the scheme.

  • Keywords

Equilibrium problem, Iterative method, Fixed point, Variational inequality.

  • AMS Subject Headings

47H10, 47J25, 47H09, 65J15, 46T20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Msh_yazdi@yahoo.com (Maryam Yazdi)

S.Hashemi@ualberta.ca (Saeed Hashemi Sababe)

  • BibTex
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  • TXT
@Article{JCM-41-153, author = {Yazdi , Maryam and Hashemi Sababe , Saeed}, title = {A Hybrid Viscosity Approximation Method for a Common Solution of a General System of Variational Inequalities, an Equilibrium Problem, and Fixed Point Problems}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {41}, number = {1}, pages = {153--172}, abstract = {

In this paper, we introduce a new iterative method based on the hybrid viscosity approximation method for finding a common element of the set of solutions of a general system of variational inequalities, an equilibrium problem, and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert space. We prove a strong convergence theorem of the proposed iterative scheme under some suitable conditions on the parameters. Furthermore, we apply our main result for W-mappings. Finally, we give two numerical results to show the consistency and accuracy of the scheme.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2106-m2020-0209}, url = {http://global-sci.org/intro/article_detail/jcm/21174.html} }
TY - JOUR T1 - A Hybrid Viscosity Approximation Method for a Common Solution of a General System of Variational Inequalities, an Equilibrium Problem, and Fixed Point Problems AU - Yazdi , Maryam AU - Hashemi Sababe , Saeed JO - Journal of Computational Mathematics VL - 1 SP - 153 EP - 172 PY - 2022 DA - 2022/11 SN - 41 DO - http://doi.org/10.4208/jcm.2106-m2020-0209 UR - https://global-sci.org/intro/article_detail/jcm/21174.html KW - Equilibrium problem, Iterative method, Fixed point, Variational inequality. AB -

In this paper, we introduce a new iterative method based on the hybrid viscosity approximation method for finding a common element of the set of solutions of a general system of variational inequalities, an equilibrium problem, and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert space. We prove a strong convergence theorem of the proposed iterative scheme under some suitable conditions on the parameters. Furthermore, we apply our main result for W-mappings. Finally, we give two numerical results to show the consistency and accuracy of the scheme.

Yazdi , Maryam and Hashemi Sababe , Saeed. (2022). A Hybrid Viscosity Approximation Method for a Common Solution of a General System of Variational Inequalities, an Equilibrium Problem, and Fixed Point Problems. Journal of Computational Mathematics. 41 (1). 153-172. doi:10.4208/jcm.2106-m2020-0209
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