Approximating a solution of an equilibrium problem by Viscosity iteration involving a nonexpansive semigroup

Binayak Choudhury; Subhajit Kundu

doi:10.4067/S0719-06462013000300002

Approximating a solution of an equilibrium problem by Viscosity iteration involving a nonexpansive semigroup

Authors

Binayak Choudhury Bengal Engineering and Science University, Shibpur Department of Mathematics, P.O.: B. Garden, Shibpur, Howrah - 711103, West Bengal, India.
Subhajit Kundu Bengal Engineering and Science University, Shibpur Department of Mathematics, P.O.: B. Garden, Shibpur, Howrah - 711103, West Bengal, India.

DOI:

https://doi.org/10.4067/S0719-06462013000300002

Keywords:

Equilibrium problem, Nonexpansive semigroup, Viscosity iteration, Fixed point, Weak convergence, Hilbert space

Abstract

In this paper we have defined a new iteration in order to solve an equilibrium problem in Hilbert spaces. The iteration we have introduced is a viscosity type iteration and involves a semigroup of nonexpansive operators. We have established that depending on some control conditions, our iteration strongly converges to a solution of the equilibrium problem.

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Published

2013-10-01

How to Cite

[1]

B. Choudhury and S. Kundu, “Approximating a solution of an equilibrium problem by Viscosity iteration involving a nonexpansive semigroup”, CUBO, vol. 15, no. 3, pp. 09–18, Oct. 2013.