# A viscosity type iteration by weak contraction for approximating solutions of generalized equilibrium problem

Volume 5, Issue 3, pp 243--251
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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.

### 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, 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

•  46C05
•  47H10
•  91B50

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