Viscosity approximation method for a variational problem
Volume 16, Issue 4, pp 208--221
http://dx.doi.org/10.22436/jnsa.016.04.02
Publication Date: October 26, 2023
Submission Date: May 05, 2023
Revision Date: September 05, 2023
Accteptance Date: September 23, 2023
Authors
R. May
- Mathematics Department, College of Science, King Faisal University, P.O. 380, Ahsaa 31982, Kingdom of Saudi Arabia.
Abstract
By combining the works of Moudafi [A. Moudafi, J. Math. Anal. Appl., \(\textbf{241}\) (2000), 46--55] and Iiduka and Takahashi [H. Iiduka, W. Takahashi, Nonlinear Anal., \(\textbf{61}\) (2005), 341--350], we introduce an iterative process that converges strongly to a particular solution of a variational inequality problem. We also study the stability of the algorithm under relatively small perturbation and we apply the obtained results to the study of a constrained optimization problem and a problem of common fixed points of two nonexpansive mappings. Some numerical experiments are provided to study the affect of some parameters on the speed of the convergence of the considered algorithm.
Share and Cite
ISRP Style
R. May, Viscosity approximation method for a variational problem, Journal of Nonlinear Sciences and Applications, 16 (2023), no. 4, 208--221
AMA Style
May R., Viscosity approximation method for a variational problem. J. Nonlinear Sci. Appl. (2023); 16(4):208--221
Chicago/Turabian Style
May, R.. "Viscosity approximation method for a variational problem." Journal of Nonlinear Sciences and Applications, 16, no. 4 (2023): 208--221
Keywords
- Hilbert spaces
- variational inequality problem
- nonexpansive mapping
- inverse strongly monotone mappings
MSC
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