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

Choudhury, B. S.¹ ; Kundu, Subhajit²

¹ Faculty of Bengal Engineering and Science University, Shibpur; P. O. - B. Garden, Howrah; Howrah-711103, West Bengal, India
² Department of Mathematics, Bengal Engineering and Science University, Shibpur; P. O. - B. Garden, Howrah; Howrah - 711103, West Bengal, India

Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 3, p. 243-251.

Résumé

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.

Détail

DOI : 10.22436/jnsa.005.03.08

Classification : 46C05, 47H10, 91B50
Keywords: Generalized Equilibrium problem, Viscosity approximation methods, Nonexpansive mappings, Weak contraction

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