Open Access

On the Existence and Convergence of Approximate Solutions for Equilibrium Problems in Banach Spaces

Journal of Inequalities and Applications20072007:017294

DOI: 10.1155/2007/17294

Received: 15 June 2006

Accepted: 20 February 2007

Published: 21 March 2007


We introduce and study a new class of auxiliary problems for solving the equilibrium problem in Banach spaces. Not only the existence of approximate solutions of the equilibrium problem is proven, but also the strong convergence of approximate solutions to an exact solution of the equilibrium problem is shown. Furthermore, we give some iterative schemes for solving some generalized mixed variational-like inequalities to illuminate our results.


Authors’ Affiliations

Department of Mathematics, Sichuan University
Department of Mathematics, Sichuan University of Sciences and Engineering
Department of Mathematics and Statistics, Curtin University of Technology


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© Nan-Jing Huang et al. 2007

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