A viscosity type iteration by weak contraction for approximating solutions of generalized equilibrium problem
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Authors
B. S. Choudhury
- Faculty of Bengal Engineering and Science University, Shibpur; P. O. - B. Garden, Howrah; Howrah-711103, West Bengal, India.
Subhajit Kundu
- Department of Mathematics, Bengal Engineering and Science University, Shibpur; P. O. - B. Garden, Howrah; Howrah - 711103, West Bengal, India.
Abstract
Viscosity iterations which include contraction mapping have been widely used to find solutions of equilibrium
problems. Here we introduce a modification of the viscosity iteration scheme by replacing the contraction
with a weak contraction. Weakly contractive mappings are intermediate to contractive and nonexpansive
mappings and are known to have unique fixed points in complete metric spaces. We apply this iteration to
the case of a generalized equilibrium problem. The special case where the weak contraction is a contraction
has also been discussed.
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ISRP Style
B. S. Choudhury, Subhajit Kundu, A viscosity type iteration by weak contraction for approximating solutions of generalized equilibrium problem, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 3, 243--251
AMA Style
Choudhury B. S., Kundu Subhajit, A viscosity type iteration by weak contraction for approximating solutions of generalized equilibrium problem. J. Nonlinear Sci. Appl. (2012); 5(3):243--251
Chicago/Turabian Style
Choudhury, B. S., Kundu, Subhajit. "A viscosity type iteration by weak contraction for approximating solutions of generalized equilibrium problem." Journal of Nonlinear Sciences and Applications, 5, no. 3 (2012): 243--251
Keywords
- Generalized Equilibrium problem
- Viscosity approximation methods
- Nonexpansive mappings
- Weak contraction
MSC
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