A viscosity type iteration by weak contraction for approximating solutions of generalized equilibrium problem
Authors
B. S. Choudhury
 Faculty of Bengal Engineering and Science University, Shibpur; P. O.  B. Garden, Howrah; Howrah711103, 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.
Share and Cite
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, 243251
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):243251
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): 243251
Keywords
 Generalized Equilibrium problem
 Viscosity approximation methods
 Nonexpansive mappings
 Weak contraction
MSC
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